Some fruits you can get seeds to grow from (though many things will have immature or unviable seeds, and those that *do* come from seed may not come reliably true to variety, but if it's just a Project then who cares <g>)
I've grown, what, clementines and kumquats and chili peppers from seed, you should be able (SOMEtimes) to do ripe red peppers (or other colors, as long as they are fully ripe or overripe), also tomatoes, presumably other things are possible (I'd guess some melons at least). Dried beans and grains, too.
You can, as a project, grow "sorta" carrots (very small) from a carrot in very good fresh condition with some green sprouts left on it, by cutting it near the top so that a thin slice of root is included in the crown and then rooting it as you would a cutting. In time it will grow multiple smallish roots you can eat. I have read this can be done repeatedly from the same carrot, tho have not done that myself.
Presumably jerusalem artichokes could be planted as with potatoes, tho have not done it myself.
(edited to add grade-school flashback: sweet potato and avocado, of course!

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Pat