Set 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 with cut sides 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.
Heat a large skillet over medium-high heat. Add beef, chili powder, garlic, cumin, oregano, cayenne pepper, paprika, chipotle pepper, salt, and black pepper. Cook and stir until beef is no longer pink, about 4 minutes. Add onion; cook until slightly softened, about 2 minutes. Add tomatoes with green chiles; cook until onions are translucent, about 5 minutes more. Let beef mixture cool.
Preheat oven to 350 degrees F (175 degrees C). Spray a casserole dish with cooking spray.
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.