Preheat oven to 350°F. Melt the butter in large nonstick skillet over medium. Add bell peppers and onions and sauté until tender, about 4 to 5 minutes. Stir together eggs and the next 3 ingredients in a medium bowl. Add the egg mixture to bell pepper mixture in the skillet, and cook, without stirring, until the eggs begin to set on the bottom, about 1 to 2 minutes. Draw a spatula across the pan to form large curds. Cook, stirring occasionally until eggs are thickened, about 6 to 7 minutes. (Don't over-stir!)

Spread 2 tablespoons of salsa verde in the center of each tortilla. Spoon about 1/4 cup egg mixture over salsa and sprinkle with 2 tablespoons cheese and 1/2 teaspoon cilantro. Roll up the enchilada and place it, seam side down, in a lightly greased 13- x 9-inch baking dish. Add Cheese Sauce and remaining cheese.

Bake in the preheated oven until sauce is bubbly, 30 minutes. Serve with your favorite toppings.