The short list, and the three different reasons for it

The list, sorted by reason

Here is the whole thing. Read the heading each item sits under, because the heading is the information.

Tested, and the answer was no

A hazard has been characterised for each of these, and there is published work behind the refusal.

Pumpkin butter, and any mashed or puréed pumpkin or winter squash. Measured as high as pH 5.4 in home-made batches, with unpredictable variation in thickness and water content, so no single process can be calculated [F-9.3]. NCHFP's instruction is "Do not mash or puree." The cubed pulp has a tested process; the purée does not.

Dense purées and starch-thickened foods generally. Refried beans, mashed potatoes, mashed squash, soups and pie fillings thickened with flour or cornstarch, pasta and rice in jars. The mechanism is heat transfer: dense purées prevent heat penetration and starch interferes with heat transfer during processing [F-9.4].

Bread and cake baked in canning jars. Clemson Extension strongly discourages it, and goes as far as saying that if you are given a home-canned cake or bread product you should assume it is unsafe and discard the contents [F-9.5]. Jar manufacturers do not endorse baking in their jars either.

Any tested recipe with the covering liquid left out. NCHFP added this to its not-recommended page in its own words: canning vegetables or any food pieces without the covering liquid used in the process research can result in under-processing, and in the case of vegetables, a risk of botulism [F-9.12]. The liquid is not a garnish. It is part of how heat gets to the middle of the jar, and the schedule was calculated with it in there.

Tender vegetables — with an asterisk. Broccoli, cauliflower, eggplant and summer squash are often listed here, and Penn State does list them, but the reason is that the process needed to destroy botulinum spores would make them mushy [F-9.11]. That is a texture finding, not a safety one. It is on this page only so you know why it is not on the same footing as the items above.

Never tested at all

No thermal process work was ever done. There is no time and no pressure to give you, and that is a gap in the research rather than a verdict on the food.

Butter. The circulating directions are not a canning process — no heat is applied to the filled jar [F-9.2]. NCHFP declines to recommend one because butter is low-acid and fat can shield spores from heat, and because no database exists that would tell anyone what the risk is [F-9.2] [F-14.11].

Milk, cream and cheese. Milk is named in the guide's own list of low-acid foods [F-9.1], and Penn State states that dairy foods are low acid and support the growth of Clostridium botulinum spores at room temperature [F-9.1]. The low-acid classification is settled. The absence of a home process is the part that was never filled in.

Herbs in oil, and pesto. Both components are low-acid, and there are no canning recommendations for either [F-9.6]. Oil coats whatever sits in it and excludes air, which is the condition the organism needs.

Eggs, plain or pickled, for shelf storage. Penn State names them as having no research-tested recipe for home canning with shelf storage [F-9.10]. Refrigerator pickled eggs are a different food and a different question.

Re-canning food that was already canned. NCHFP has no safe tested processes for it, and explains that already-cooked food packs more tightly and softens, so heat distributes through the jar differently than it did in the process research [F-9.7].

Tested once, then withdrawn

One item, and it is the most interesting thing on the page.

Shelled nutmeats in a dry pack. There was a University of Georgia process. It is withdrawn. The reason given is that it produced a vacuum-sealed jar with no documentation of microbial sterilisation, and that newer Salmonella research on low-moisture foods made the gap matter [F-9.8]. There is no substitute process at this time [F-14.10].

Why the three categories are worth the trouble

Two practical consequences, and one about how you read.

The first is what to expect from the future. A never-tested item can become a tested one if somebody runs the work. A characterised hazard usually does not go away. If you are wondering whether to keep checking back on butter, the answer is that it is possible; if you are wondering the same about pumpkin butter, it is much less likely.

The second is how to argue with a page that says otherwise. A blog that says "the USDA has tested canning butter and found it dangerous" is wrong, and so is a blog that says "there is no evidence against it, so it is fine." Both have collapsed the same distinction in opposite directions. The accurate sentence is short: nobody has done the work, so nobody has a number, so there is nothing to follow.

The third is about how confident a page sounds. Confidence is not evidence, in either direction. The most trustworthy paragraph quoted on this page is the one where a research centre says it does not have the data. A page that never says that about anything has either read very narrowly or is not telling you when it is guessing.

What actually happens to the food

Every item above has somewhere else to go, and this is not a consolation prize. Freezing preserves flavour better than canning for most of these foods anyway.

Dense purées, pumpkin butter, refried beans and mashed vegetables all freeze well. Dairy freezes with a texture change and refrigerates without one. Herb oils and pesto are refrigerator foods with a short window, and pesto freezes in ice-cube trays about as well as anything does. Nuts belong in the freezer regardless of any of this, because their real enemy on a shelf is rancid fat. Bread freezes. Eggs keep in a fridge.

And where a food has a tested form that is close to what you wanted — cubed pumpkin instead of purée, whole potatoes instead of mashed, dilled beans instead of plain ones — that route exists precisely because somebody did the work on it. Take the schedule from the tested source and not from here.

If you have already done one of these

That is a common position and it is not a stupid one. The pages teaching these methods are confident, well photographed and often better written than the Extension pages that contradict them, and several of them rank above the tested sources for the obvious searches.

Do not taste a jar to find out. The organism at issue does not reliably announce itself by smell, appearance or bulging, and a sealed lid tells you a vacuum formed rather than that anything reached a temperature [F-1.9]. What canning actually does, in the guide's own order, is remove oxygen, destroy enzymes, prevent the growth of undesirable organisms — and form a vacuum, which is listed last and is a consequence rather than the mechanism [F-1.9].