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 turkey, the onions, green peppers, and garlic and cook until the turkey is no longer pink and is cooked through, about 8 minutes. Drain off any excess fat and sprinkle the meat mixture with the cumin.
Add the beans, tomatoes, chiles and adobo sauce to the skillet and bring to a boil over high heat. Reduce the heat to medium and simmer until heated through and slightly thickened, about 5 minutes. Remove pan from the heat and stir in the cheese and cilantro.
Spread the turkey 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 and spread the cornbread batter over the turkey mixture and bake until the cornbread is golden-brown, 20 to 25 minutes. Let the tamale pie stand for 5 minutes before cutting into squares and serving.