Serve these eggs with Salsa Fresca (click here for recipe).

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Preheat the broiler.

Heat the tortillas by toasting them one at a time in a dry cast-iron skillet or directly over a gas flame until lightly toasted. Place on a baking sheet; spread each tortilla with 1/4 cup of refried beans, and cover to keep warm.

Working in batches as needed, heat the butter in a large skillet over medium-high heat until it is very hot but not smoking and the foaming has subsided. Crack the eggs directly into the hot butter and reduce the heat to medium-low or low. Fry the eggs, shaking the pan occasionally to keep the eggs from sticking. Season the eggs with salt and pepper. Fry about 2 minutes for "sunny-side up," 3 minutes for medium yolks, and 3 1/2-4 minutes for hard yolks.

Top each prepared tortilla with 2 fried eggs and 2 tablespoons of the grated cheese. Slide the tortillas under the broiler to melt the cheese.

Meanwhile, dice the avocados and toss with the lime juice to prevent the avocados from discoloring. Divide the avocados among the tortillas. Top each serving with 2 tablespoons salsa and 2 tablespoons sour cream. Garnish each serving with 1 cilantro leaf serve.