Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish with cooking spray.
Combine Alfredo sauce and salsa verde in a bowl.
Arrange eight tortilla halves in the prepared baking dish, to mostly cover the bottom of the dish.
Spread 1/3 of cooked chicken evenly over the tortillas. Pour 1/3 of Alfredo mixture on top of cooked chicken, then sprinkle with 2/3 cup of Monterey Jack cheese. Repeat the layers 2 more times, ending with the remaining cheese on top.
Bake in the preheated oven until heated through and the cheese is melted, about 25 minutes.
Let stand 5 minutes before serving. Garnish with fresh cilantro and tomatoes, if desired. Recipe developed by Ashley Sandoval