Place the poblano peppers on a baking sheet and broil them, turning every few minutes, until the skins blister and darken on all sides, 8 to 12 minutes.

Meanwhile, heat the olive oil in a large skillet over medium heat. Cook the onion for 3 to 4 minutes, until softened. Add the ground chicken, sprinkle with the taco seasoning and cook, breaking it up, until browned and cooked through to 165°F. Season with 1/2 teaspoon of the salt and the pepper and take the skillet off the heat.

Move the roasted peppers to a large bowl and cover it with a plate or towel for 10 minutes. Peel off the loose skins, remove the stems and seeds, and slice the peppers into wide strips.

Heat the oven to 375°F and lightly grease a 9x13-inch baking dish with olive oil. Spread half of the poblano strips in the dish, spoon the chicken over them and sprinkle with half of the cheddar and Monterey Jack. Add the rest of the poblano strips and the rest of the cheese.

Whisk the eggs, milk, flour, baking powder and the remaining 1/2 teaspoon salt until mostly smooth; a few small flour lumps are fine.

Pour the egg mixture evenly over the casserole. Bake for 35 to 40 minutes, until the center is set and no longer jiggles, the edges are lightly golden and the center reaches 165°F.

Let the casserole rest for 10 minutes before slicing. Serve with salsa verde, cilantro, avocado, green onions and sour cream.