Pre-heat the oven to 350° F, and grease a 9x13 baking dish.
Cut the tortillas into quarters or triangles and set aside.
In a large skillet, sauté the onion in the olive oil 'til the onion softens, about 5-7 minutes.
Add the ground beef to the onion, and brown for about 20 minutes over low to medium heat. Drain the oil off the meat when browned.
In a large bowl, mix together the soups, enchilada sauce, and green chiles.
In the prepared 9x13 baking dish, layer in this order (you'll be repeating this step, so save enough ingredients for a second layering): tortillas, meat, cheese, soup mixture.
Repeat the layers.
Cover the casserole with aluminum foil, and bake at 350° F for about 25 minutes. Then uncover and bake an additional 20-30 minutes, 'til the casserole is bubbly and well heated all the way thru.
Serve with sour cream if desired.