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1
Place all sauce ingredients except for the oil, agave, and salt into a blender and blend until smooth. Heat oil in a large sauce pan over medium, adding the blended sauce and stirring to thicken. Stir in the agave and salt. Here you will run into your first big hurdle, which is to not drink all of the sauce or to eat the whole lot straight from the saucepan with a bag of Tostitos. Resist. (The sauce can be made ahead of time, cooled, and stored in the fridge up to a day in advance.)
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2
Assemble your chilaquiles! This is a little free-form amounts-wise; you will end up with about 2 cups sauce, which can make a dish for anywhere from 3 to 6 people depending on how saucy you like things. Adjust the tortilla/cheese/egg amounts accordingly.
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3
Preheat the broiler, and then start frying tortillas. Heat 1/4 inch of oil in a saucepan and, working in batches, fry the tortilla triangles, flipping halfway through, until a little crisp but not totally crunchy. You are not making chips, but instead like 3 notches less crispy than that; this way, the tortilla can hold up to the soupy addition of sauce/cheese/egg, but also sort of melt away into that. I know this sounds crazy. Just trust.
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4
Drain tortillas on a paper towel, sprinkling lightly with salt. Second hurdle time: Now you don't even need the bag of Tostitos because you made almost-chips! Can't you just eat all the sauce now with these??? No. You cannot. Press on.
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5
In your vessel of choice (for more of a crowd, use a casserole dish or a cast iron skillet; for less, a pie pan or even a sizzle plate works), layer a bunch of tortillas, overlapping as you go. Spoon sauce over them to desired slatheriness (I like a lot), and then cover with both cheeses (again, I like a lot. I mostly always like a lot). This is allowed to look a little soupy -- in fact, it should. Broil until cheese is melted. DO NOT take a fork to this yet. One more step!
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6
Fry eggs over easy in a small pan, keeping yolks intact and uncooked because you know what's up. Scoop amounts of the saucy tortilla mess into a bowls, add an egg (or two), some fresh cilantro, and salt and pepper. DONE! At long last. Now eat.
