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To make the salsa verde: Put the tomatillos, chile, onion, and garlic in a medium pot and add water to cover.
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Bring to a boil over high heat.
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Reduce the heat to medium-low and simmer until the vegetables are soft and the tomatillos turn pale green, 15 to 20 minutes.
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4
Remove from the heat and let cool slightly.
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5
Carefully transfer the boiled vegetables, along with the cooking water, to a blender.
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Puree for a few seconds to blend; be sure to hold down the lid with a kitchen towel for safety.
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Add the 1/2 bay leaf, oregano, thyme, salt, and broth.
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Continue to puree until smooth.
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You should have about 1 quart of salsa verde.
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Place a wide pot or pan over medium-high heat and coat with the corn oil.
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When the oil is hazy, pour in the salsa verde; it will bubble a bit.
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Reduce the heat to medium and simmer, stirring occasionally, until the sauce is slightly thickened, 10 to 15 minutes.
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13
Cover, reduce the heat to very low, and keep warm while you finish the chips.
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Pour the vegetable oil into a heavy-bottomed pot or countertop deep fryer to a depth of about 2 inches and heat to 375F over medium-high heat.
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15
Stack the tortillas and fan them with your thumb to separate.
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Cut the tortillas into 8 wedges like a pie.
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Working in batches, fry the tortilla chips, turning them with a skimmer or slotted spoon so they don't stick together, until golden brown, about 2 to 3 minutes.
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Remove the chips to a paper towel-lined baking pan or brown paper bag to drain and cool.
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(Let the oil return to the proper temperature between batches.)
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20
To finish the chilaquiles, uncover the salsa verde and raise the heat to medium.
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21
Just when it starts to bubble, stir in the beaten eggs.
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Cook and stir for about 5 seconds, until the egg feathers into the sauce, thickening and binding it.
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23
Immediately add the chips, tossing gently until they have absorbed enough sauce to become soft.
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24
Take care not to break the chips.
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25
Sprinkle the Jack cheese on top and let it melt.
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26
Divide the chilaquiles among 4 plates.
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27
Sprinkle with the queso fresco, chopped onion, and cilantro.
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Garnish with the crema fresca and serve immediately.