Remove eggs from stovetop while they're still a bit wet; they'll finish cooking in the oven. To make this a day ahead, go through Step 2; cover and chill the casserole. Let stand at room temperature about 20 minutes before baking.
Preheat oven to 350°F. Melt butter in large nonstick skillet over medium. Add bell peppers and onions; sauté until tender, 4 to 5 minutes. Stir together eggs and next 3 ingredients in a medium bowl. Add egg mixture to bell pepper mixture, and cook, without stirring, until eggs begin to set on bottom, about 1 to 2 minutes. Draw a spatula across pan to form large curds. Cook, stirring occasionally, until eggs are thickened, about 6 to 7 minutes. (Do not overstir.)
Spread 2 tablespoons salsa verde in center of each tortilla. Spoon about 1/4 cup egg mixture over salsa; sprinkle with 2 tablespoons cheese and 1/2 teaspoon cilantro. Roll up, and place, seam side down, in lightly greased 13- x 9-inch baking dish. Add Cheese Sauce and remaining cheese.
Bake in preheated oven until sauce is bubbly, 30 minutes. Serve with desired toppings.