Preheat the oven to 375° Fahrenheit.
Heat vegetable oil in a large skillet over medium-high heat, reduce to medium, add and brown the ground beef until no pink pieces remain. Drain any excess fat, transfer to a bowl, and set aside.
Add the onion to the skillet and cook for 2 minutes, then the garlic and cook for an additional minute.
Add the ground beef back in, can of green chilis, salt, pepper, cumin, chili powder, paprika, and salt and pepper. Stir to combine, cook for about 4 minutes, and remove the pan from the heat.
Combine the Monterey Jack and Cheddar cheese in a small bowl and set aside.
Spread a thin layer (one ladle, about ½ cup) of enchilada sauce to fully coat the bottom of a casserole dish.
Place 6 tortillas in the baking dish on top of the enchilada sauce, and then add another ladle (½ cup) of enchilada sauce. Top with ⅓ of the beef mixture and then ⅓ of the cheese mixture.
Repeat the layers twice. To the last layer, add any remaining cheese.
Cover the casserole dish with foil and bake for 30 - 40 minutes. Uncover and bake an additional 10 minutes longer to brown the cheese.