Preheat the oven's broiler and place the rack about 6 inches from the heat source. Line a baking sheet with aluminum foil. Roast the peppers on the baking sheet for 10-15 minutes, turning occasionally, until the skins are blackened and charred. (Tip: Keep an eye on the peppers to prevent burning!)
Transfer the roasted peppers to a plastic bag and let them steam for about 10 minutes. Peel off the skin, remove the stems, open them up, and remove the seeds.
Preheat the oven to 350°F. Lightly coat a 3-quart baking dish with nonstick spray.
Arrange half of the roasted chiles in the baking dish in a single layer. Sprinkle 1 cup of jack cheese and 1/2 cup of cheddar on top. Repeat the layers once.
In a medium bowl, whisk together the eggs, milk, flour, baking powder, onion powder, garlic powder, salt, and pepper until well combined. Pour the mixture evenly over the cheese and chiles.
Bake in the oven for 45 minutes until puffed up in the center and the eggs are set and golden around the edges. (Tip: A toothpick inserted in the center should come out clean when done.)
Let it cool for 5-10 minutes before cutting. Slice into squares and serve with sour cream, salsa, and freshly chopped cilantro. Enjoy!
Notes
For a spicier version, you can leave some of the poblano pepper seeds in.