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Even in Mexico (or is it especially in Mexico?), chilaquiles—the dish of fried corn tortillas soaked in hot salsa—are known as a cure for the common hangover. It's got a number of things going for it. It's easy to make, and consists almost completely of leftovers, so even in the haze of the-morning-after, you should be able to hold yourself together long enough to whip up a batch.
It's plenty fatty, what with the deep-fried chips and topping of queso cotija or crema (I like them both). If you make your salsa right, it should have heat to spare, and it's fully customizable. Leftover refried beans? Pile 'em on. Need some extra protein? Add some scrambled or fried eggs. Big on meat? Go ahead and crumble on some chorizo, or add some pulled strips of leftover roast chicken. Avocado makes for a fine side.
Personally, I like to up the heat with rajas, green chiles blackened over the burner, peeled, and sliced into thin strips. (You can use plain old poblanos from the supermarket if you don't have access to any of the fancy-pants varieties—I use them).
Though chilaquiles superficially resemble nachos or even Tex-Mex style migas, they actually predate nachos by several centuries—the name comes from the Nahuatl.
Some folks like their chilaquiles crisp, tossing them in sauce immediately before consuming. I prefer to throw my fried tortillas into a pot of simmering sauce, toss 'em around, and let 'em stew for a few minutes until tender and swollen but still crisp in the center. It's tough to get this texture with commercial chips, so if you've got the wherewithal, I'd suggest deep frying your own. It makes for a much more satisfying experience.
Bottled green salsa works just fine, but making your own the night before is pretty simple. If you know you're gonna need it in the morning, I'd spend the time to do it.
Check out the full recipe here.