Grease an 8-inch baking dish with the butter and set it aside.
Heat the olive oil in a nonstick skillet over medium heat. Add the ground beef, onions, green peppers, and garlic. Cook until the ground beef is no longer pink and cooked through. Drain off any excess fat and sprinkle the meat mixture with the cumin.
Add the beans, tomatoes, chilies and adobo sauce to the skillet and bring to a boil over high heat. Reduce heat to medium low and simmer until slightly thickened (5 minutes). Remove pan from the heat and stir in the cheese and cilantro.
Spread the meat mixture in the prepared baking dish, pressing down on it with the back of a spoon to make an even, compact layer.
Combine the cornbread mix with milk and egg. Spread the cornbread batter over the beef mixture and bake until the cornbread is golden-brown, 20-25 minutes. Let the tamale pie stand for 5-10 minutes before cutting into the squares and serving.