Heat oven to 400° F. In a large skillet, over medium heat, cook the sausage, crumbling it with a spoon, until no trace of pink remains, about 7 minutes.
Add the chili powder and cook for 1 minute. Spoon off and discard any fat.
Add the beans, tomatoes, and salsa and simmer for 3 minutes.
Meanwhile, in a bowl, combine the corn bread mix, egg, and milk, then stir in the Cheddar.
Transfer the chili to a 9-by-9-inch or 11-by-7-inch 2-quart baking dish. Spread the corn bread batter over the top.
Bake until golden, 15 to 20 minutes. Let cool for 5 minutes before serving.