I have a tried and true onion tart recipe that could easily be done crustless, but I'm wondering if wilting the onions might be an issue sans salt. Might be worth a try. Here's a quick adaptation, untested. You're OK with wine, I'm hoping?
Slice 3# of white or yellow onions thinly, and cook in a large pan over medium-high heat with a generous dusting of black pepper, coating with 2T butter and 2T olive oil (more if needed to coat all). Normally, salt would be added for flavor and to sweat the onions, but the heat alone should draw out a good bit of liquid. The idea is to keep cooking off the liquid and then adding liquid until you have repeatedly broken the spirit of the onions and cooked them down to about 1" - 1 1/2" depth. But you don't necessarily want them to caramelize. A little browning is fine, but keep adding just enough wine to avert caramelization, and cook without a lid to allow liquids to steam off.
Once cooked down to a sweet, peppery mass (45 min?), allow to cool. You can prepare the custard simultaneous to the stirring of the onions. Use whatever ratio you like for the custard, but I would usually have 5-6 eggs and a healthy splop of heavy cream, a shake of nutmeg, a pinch of cayenne if you wish, and a grating of Parm if the salt does not bother you (really can be omitted or a lower-salt cheese used just for a little flavor). Combine with onions and bake ~25 minutes at 350F or until set.
The sweetness from the wine and onions combined with the pepper punch is exquisite. It's sort of like French onion soup quiche.
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