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Set the oven rack about 6 inches from the heat source and preheat the oven’s broiler. Line a baking sheet with aluminum foil. Place poblano peppers cut-side down onto the prepared baking sheet.
Cook under the preheated broiler until poblano pepper skins have blackened and blistered, 5 to 8 minutes. Place blackened peppers into a bowl and cover tightly with plastic wrap. Allow peppers to steam as they cool, about 10 minutes.
Run water over the poblano peppers to remove skins and discard them; drain peppers on paper towels. Place a layer of peppers on the bottom of the prepared dish; place 1/3 of the beef mixture on top. Cover with 1 cup shredded Mexican cheese blend. Repeat layers twice more in the same order.
Bake, uncovered, in the preheated oven until golden brown on top, about 35 minutes
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