Roast the poblanos over an open flame or under the broiler until charred all over, turning as necessary, about 8 minutes. Put in a bowl and cover with plastic wrap to steam and loosen the skin, about 5 minutes. When cooled, remove the stems and run under cold water to peel off the blackened outer skin and remove the seeds.
Preheat the oven to 350 degrees F.
Put 1 piece Colby Jack cheese in the center of each pepper. Pour half of enchilada sauce into an 8-inch square baking dish. Put half of the cheese-filled peppers on top of the enchilada sauce. Repeat with the remaining sauce and peppers.
Beat the eggs in a large bowl until very frothy. Whisk in the Cheddar, milk, flour and baking powder. Gently pour the mixture over the peppers and sauce in the baking dish.
Bake until the casserole is set in the center and golden brown all over, about 1 hour. Let rest for 5 minutes. Serve warm.
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