Preheat your broiler and place the rack 6 inches from the heat source. Arrange the poblano peppers on a foil-lined baking sheet and broil for 10-15 minutes, turning occasionally until the skins are charred and blistered.
Transfer the charred peppers to a plastic bag and seal it to steam for about 10 minutes. This makes peeling easier. Afterward, peel the peppers, remove the stems and seeds, and open them flat.
Set your oven to 350°F (175°C) and grease a 3-quart casserole dish.
Place half of the prepared chiles in the bottom of the dish, cover with 1 cup of Monterey Jack and ½ cup of cheddar cheese. Repeat the layers with the remaining chiles and cheese.
In a bowl, whisk together the eggs, milk, flour, baking powder, onion powder, garlic powder, salt, and pepper until smooth. Pour this mixture evenly over the chile and cheese layers.
Bake the casserole for approximately 45 minutes, or until the top is golden and the center is set.
Let the casserole cool slightly before cutting into squares. Serve with sour cream, your choice of salsa, and a sprinkle of fresh cilantro for added flavor.
