What cooked foods will stay fresh with no fridge for a month?

None of the above cooked foods will last a month, bread will be moldy in less than a week, cake and jelly will get moldy too once it is opened.

Dried fruits and nuts. Also peanut butter and chocolate bars.

Big Macs; “chicken” McNuggets.

Canning cooked goods will keep them from spoiling, but somehow I don’t think that’s what you’re looking for.

Potato chips are cooked, aren’t they?

More than a type of food, you’re looking for storage options.

For anything to last outside refrigeration, it needs to be dry and/or airless. Potato chips have most of their moisture removed, so they can last as long as they’re not exposed to moist air which will make them go stale. Cooked vegetable and fruit preserves will last as long as they are vacuum-sealed. Same for meat jerkeys.

I’d consider pickling a form of cooking, even though no heat is applied, because it does result in a chemical change to the food product. The vinegar brine prevents microbial decay of the food, so that might be one option.

We leave jellies and preserves out 24/7 and they never go bad. lol And bread, at least ours, stays out well over a week without going moldy.

Where do you live?

I’m in Florida, land of heat and humidity.

When I lived in New York, we kept butter out on the counter in a butter dish all the time. If I do that here, it melts and goes rancid within a day.

Region comes into play. bread gets moldy in some environments, in others it just dries out. I have lived in both such environments. a friend once taught me that sucking the air from the bag each time before twisting it closed,extends the life of the loaf by two to four times. It works.
You have to take into account your environment, packaging, cooking methods.
I have worked in the fast food industry in my lifetime. I learned that if I brought home leftover cheeseburgers, they stored well in the freezer for a while, but dried out rapidly in the frig.
Frizzen is fine, but reheating makes them a bit goopy.

Twinkies.

Jellies and jams should stay good as you pointed out. Bread no way, not anywhere I have ever lived, unless you include putting it out in the cold during the winter in the below freezing weather.

Things like beef jerky, but I would keep it in plastic. I guess I would keep everything in some sort of packaging.

Crackers, chîps, and cookies made with a lot of fat.

It would really help to know the purpose and storage of these foods. Are you trying to find things to help a homeless person? Are you currently living without electricity? Are you putting together emergency rations? Are you sending FPO?

cooked and then dried out, such as various meat jerky type foods and dried fruits, such as apple, banana and strawberry chips.

Fresh eggs will last a while without refrigeration. Maybe not quite a month, but they’d still be edible after 3 weeks. Of course once you cook them their shelf life drops to less than a day without refrigeration, unless you hard-boil and pickle them.

Veggies and fish can also be pickled. Pickles will keep for months without needing to be refrigerated. Certain types of dry sausage like salami and chorizo will also keep for weeks, as long as they’re whole, not sliced or cut.

Eggs will NOT be safe without refrigeration in any form except pickled more than a few hours!

Eggs are kept outside the fridge in cool climates. Not a month though.

Pretzels
Fritos
Twinkies
Oreos
etc.

@JLeslie raw eggs can keep outside of refrigeration for some indefinite time measured in days, but the OP was about “cooked” foods.

@CWOTUS Right. I did fail to remember that we are talking about cooked. Thanks for pointing it out.

Not really cooked, but any dried produce or jerked meat. Anything will keep longer if not exposed to oxygen, so you could pack whatever in those suck out the air and seal it in plastic machines.

I guess the British climate is very different from what you get in most of the US, which makes a difference to how long some things will keep.

I forgot, lots of foods preserve very nicely if packed in salt! Virginia Country Hams are fixed this way. Here’s a video. https://www.youtube.com/watch?v=Snc5AqXku_M

And the old fashioned way of making sauerkraut is another. https://www.youtube.com/watch?v=0l0joPdfV7E&list=PLF7FA81AB63BD81FB

I can only say something pickled but if you don’t open a jar though