Spiced Beef Corn Bread Cobbler

4 tablespoons vegetable oil

2 garlic cloves, finely chopped

1 pound ground beef chuck

1 teaspoon sugar

1/2 teaspoon ground cinnamon

1/2 teaspoon cayenne

1/4 teaspoon ground allspice

1/4 teaspoon black pepper

3/4 teaspoon ground ginger

1 1/4 teaspoons salt

1 (14- to 15-ounce) can diced tomatoes in juice

cup yellow cornmeal

1/3 cup all-purpose flour

1 teaspoon baking powder

1/3 cup whole milk

1 large egg

2 ounces coarsely grated sharp Cheddar ( 1/2 cup plus 2 tablespoons)