Heat the oil in a saucepan with a capacity of approximately 6quarts and add the onions and garlic. Cook, stirring, until wilted. Add the beef, breaking up lumps with the side of a heavy metal spoon. Cook, stirring, until meat loses its raw look.
Add the tomatoes, tomato paste, chicken stock, jalapeño peppers, oregano, salt, and ground pepper. Cook, stirring often, 30 or 40 minutes, until thickened. Add the cream sauce and stir.
Meanwhile, preheat the oven to 350 degrees.
Butter two8-quart casseroles. Add a layer of hominy, a layer of chicken, a layer of sauce, and a layer of cheese in each. Continue making layers, ending with a layer of cheese.
Place the casseroles in the oven and bake45 minutes, or until piping hot and bubbling throughout.