Heat the oven to 375°F and grease a 9-by-13-inch dish. Combine beans, tomatoes, chiles, tomato sauce, cumin, chili powder and 1/2 teaspoon salt in a saucepan and simmer 6 minutes; spread hot filling in the dish.
Whisk cornmeal, flour, baking powder and remaining salt.
Whisk egg, milk and butter, stir into dry ingredients just until combined, then fold in pepper Jack.
Spoon batter in small mounds over the filling and spread gently.
Bake for 30 to 35 minutes until golden and a pick in the cornbread comes out clean. Rest 10 minutes.