Step 1

Position rack about 8 inches from broiler; preheat to high. Line a baking sheet with foil.

Step 2

Place poblanos on the prepared pan. Broil, flipping once, until the skins are charred, 15 to 20 minutes. Transfer to a bowl and cover with plastic wrap. Let stand at room temperature for 10 to 15 minutes to help the skins loosen. Remove and discard the skins, stems and seeds.

Step 3

Meanwhile, whisk eggs, milk, shallot and salt in a large bowl.

Step 4

Preheat oven to 375°F. Arrange the poblanos in a 10-inch cast-iron skillet and pour the egg mixture on top. Top with cheese. Bake until the eggs are set, 20 to 25 minutes. Slice into 6 pieces and serve with toast.