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1
To make the sauce: warm the oil in a skillet over medium heat; stir in the onion and garlic; cook 2-3 minutes or until limp.
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2
Mix in the chile, tomatoes, vinegar, sugar, cumin, and salt; bring to a boil.
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3
Decrease heat to a simmer; cover and cook 15 minutes or until thickened but still spoonable.
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4
Stir in the cilantro and lime juice shortly before removing from the heat; set aside.
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5
Heat about 1/4 inch of oil in a large skillet; dip the tortillas into the oil, 1 or 2 at a time, and cook for a few seconds, until soft and pliable.
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6
Drain the tortillas and arrange 2 overlapping on each of 4 plates.
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7
Break the eggs, 2 by 2, into cups or small bowls.
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8
Pour out of the skillet all but enough oil to generously coat the surface.
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9
Warm the skillet again over medium heat for 1-2 minutes.
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10
Add 1 to 2 teaspoons of the butter, and when the foam subsides, in a about 1 minute, pour in the eggs and begin to fry them, 2 to 4 at a time, depending on the size of your skillet.
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11
Cook for 1 minute, seasoning generously with salt and pepper while the eggs cook.
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12
As they cook, use a spatula to scoop up some of the butter to drizzle over the whites.
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13
Then turn the heat down to low and continue cooking and drizzling with butter for about 1 minute or until done to your liking.
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14
Repeat with remaining eggs, adding more butter to the skillet as necessary.
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15
Top each tortilla with a fried egg; sprinkle a couple of tablespoons of the cheese over each serving of eggs and top with equal portions of the sauce.
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16
Serve the eggs immediately, with crema and cilantro.