4 poblano chile peppers, halved lengthwise and seeded
1 bunch medium spring onions, stems cut into 2inch pieces, bulbs quartered
1/4 cup masa harina (instant corn flour) or all-purpose flour
Vegetable oil, for frying (3 to 4 cups)
10 corn tortillas, cut into 2-inch pieces
8 ounces Oaxaca or muenster cheese, grated (about 2 cups)
8 large eggs
3 cups whole milk
Kosher salt and freshly ground pepper
1/2 teaspoon chili powder
Sour cream, chopped jalapenos and/or chopped cilantro, for topping (optional)
Preheat the broiler. Arrange the poblanos skin-side up on a baking sheet. Add the spring onions and broil until the poblano skins are charred and the onions are blackened around the edges, 7 to 8 minutes. Transfer the poblanos to a large bowl, cover with plastic wrap or a plate and let cool 10 minutes. Rub off the skins with your fingers, then pat dry. Roughly chop the poblanos and onion bulbs, then toss with the masa harina in a medium bowl; set aside while you fry the tortillas.
Line a baking sheet with paper towels. Heat about 1 inch of vegetable oil in a high-sided skillet or Dutch oven over medium-high heat until a deep-fry thermometer registers 350 degrees F. Working in batches, fry the tortillas, stirring, until stiff but not browned, about 5 minutes. Transfer to the paper towels to drain.
Spread half of the fried tortillas in a 3-quart baking dish. Top with half of the poblano-onion mixture and half of each cheese. Layer the remaining tortillas, poblano-onion mixture and cheeses on top.
Whisk the eggs and milk in a large bowl; whisk in 1 1/2 teaspoons salt, pepper to taste and the chili powder. Pour the egg mixture into the baking dish. Cover and refrigerate 8 hours or overnight.
Remove the dish from the refrigerator about 30 minutes before baking and uncover. Preheat the oven to 350 degrees F. Bake until the strata is lightly puffed and golden on top and just set in the center, 50 minutes to 1 hour. Let cool 10 minutes before serving. Top with sour cream, jalapenos and/or cilantro.
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