Saw a recipe for regular Chili Rellenos Casserole and got all twisty when I started making it. Didn't have beef thawed but I had chicken. Didn't have red enchilada sauce, but had salsa verdes. I used my Hatch chiles, but left the canned chiles in the recipe. It goes together super quick, and the family loved it.
Preheat oven to 350 degrees F. Grease a 9x13-inch baking dish.
Split the chiles open, and spread half the chiles into the bottom of the prepared baking dish. Top with shredded chicken. Combine the Cheddar cheese and Jack cheese, sprinkle half the cheese over chicken and top with the rest of the canned chiles. Scatter the chèvre over the top.
Beat the eggs, flour and milk in a bowl. Pour over chèvre covered casserole.
Bake in the preheated oven until set, about 30 minutes; remove casserole, and top with the remaining cheese. Pour the green chili salsa over the top; return to oven, and bake until the cheese is melted, about 15 more minutes
Serve with cilantro, lime, sour cream, and tortilla chips.