My inclination here is no, we should deem these examples off-topic under the "what can I do with X" custom close reason. If no dish would normally contain large quantities of X, however, that might fit under the "no culinary uses" exception. (That's not the case with eggs or almonds, I don't think.)
Note also that "how can I preserve X?" may well be a good question!
I do hate to ban categories questions as much as anyone, but I'm afraid that this type of question does appear to be the kind of thing that can attract a large number of equally good answers.
(This answer is not meant to be laying down the law, of course - vote and comment as you see fit!)
To back up a bit, that close reason is all about trying to avoid long-list questions (i.e. too-broad questions) but without getting into a debate about whether things are too broad on every question in this category. The exception carves out an area where there are not likely to be a lot of possibilities (so the question is less broad) and on top of that, the potential answers are not likely to be well-known (so the question is even more useful).
So in looking at these questions, we should think primarily about how broad they are, i.e. how long the list of answers would be. It seems that both the egg question and the almond question are fairly broad. There are a rather large number of possible things one can make with a lot of eggs or a lot of almonds. If they were less generic ingredients, that might be different, but these are pretty common things. So it makes sense to lump the egg question and the almond question in with the rest of "what can I do with X?"
To get an idea of how to make this all consistent, we can simply try to apply the "no culinary uses" exception. Usually we're asking "is X normally an ingredient." This is pretty much the same, except X is a large quantity of something, not just any amount. So we should then ask: is "a lot of X" something that's generally regarded as a possible ingredient in a recipe? If so, the close reason applies. If not, the exception applies.
Using those rules, we might say:
- "...a lot of eggs" - off-topic, since it's common for dishes to be mostly made of eggs.
- "...a lot of fresh mint" - on-topic, since it's uncommon for dishes to mostly be made of mint.