Brown ground beef in a large skillet over medium-high heat. Stir in onions, garlic, oregano, cumin, salt, pepper, and green chilies and cook until onions are translucent. Stir in tomato sauce. Cover and simmer over low heat for 15 minutes.
Butter a 9x13-inch pan.
Place a few spoonfuls of the meat sauce mixture on the bottom of the pan. Place 4 tortillas over sauce. Cut tortillas to fit if necessary. Spread additional sauce over tortillas. Crumble half of queso blanco over meat sauce. Top with 1 cup of pepper jack cheese. Repeat with second layer. Finish with a layer of tortillas, sauce, and pepper jack cheese.
Bake at 350°F for 45 minutes or until nicely browned and bubbly. Cool 10 minutes before cutting. Makes 6 to 8 large servings.