Preheat the oven to 350 degrees F and grease a 9 by 13-inch baking pan.
In a large skillet, cook the beef until mostly browned. Stir in onions, chiles and garlic and cook until onions have softened. Add the tomatoes, oregano and cumin and cook until the tomatoes have thickened to form a sauce about 10 minutes.
Heat the tortillas so that they are pliable--either over a gas flame or in a microwave oven.
Divide meat among the tortillas, about 1/4 cup per tortilla, and sprinkle each with cheese. Roll up tortillas and place in baking dish and top with more grated cheese. Bake for 10 minutes. Garnish with a thick salsa, sour cream and chopped cilantro if desired.