Preheat your oven to 350°F (175°C). Grease a 9×13-inch baking dish.

Roast the poblano peppers over an open flame or broil them in the oven until the skin is charred and blistered. Place them in a paper bag or a covered bowl for about 10 minutes to steam, then peel off the charred skin, remove seeds, and cut into strips.

In a mixing bowl, combine the shredded cheddar cheese, shredded Monterey Jack cheese, and diced green chilies.

In another bowl, whisk together the flour and baking powder. Gradually add the milk while stirring to avoid lumps. Beat in the eggs, salt, black pepper, and cayenne pepper until the batter is smooth.

Layer half of the poblano pepper strips in the greased baking dish. Sprinkle half of the cheese and chilies mixture over the peppers. Repeat with the remaining peppers and cheese mixture.

Pour the batter evenly over the layers in the baking dish.

Bake in the preheated oven for about 45 minutes, or until the casserole is puffed and golden brown.

Serve hot with salsa on the side.