Preheat the Oven: Preheat the oven to 350°F (180°C). For a charcoal grill, prepare the coals for indirect cooking and aim for a steady temperature of 350°F (180°C). Keep the heat source to one side and place the baking pan on the opposite side so the cornbread cooks without direct exposure to the coals.
Mix the Dry Ingredients: Add the polenta, all-purpose flour, baking soda, salt, and brown sugar to a large mixing bowl. Stir with a whisk until the ingredients are evenly combined, breaking up any lumps of brown sugar.
Add the Wet Ingredients: Pour the melted butter and buttermilk into the bowl. Add the eggs and honey, then stir until a smooth, thick batter forms. Avoid overmixing, as too much stirring can make the cornbread dense.
Fold in the Cheese: Add the shredded cheddar cheese to the batter. Use a spatula or large spoon to fold it in gently until the cheese is evenly distributed throughout the mixture.
Grease the Baking Pan: Coat an 8-inch square baking pan or a similarly sized oven-safe dish with oil or softened butter. Cover the bottom and sides, paying attention to the corners to prevent the cornbread from sticking.
Pour in the Batter: Transfer the batter to the prepared pan. Use a spatula to spread it evenly into the corners and smooth the top so the cornbread bakes at a consistent thickness.
Bake the Cornbread: Place the pan on the middle oven rack and bake for about 30 minutes. The top should look lightly golden, and the center should be set. For charcoal grilling, position the pan away from the lit coals, close the lid, and maintain a temperature near 350°F (180°C).
Test for Doneness: Insert a wooden skewer or toothpick into the center of the cornbread. If it comes out clean or with a few dry crumbs, the cornbread is ready. If wet batter sticks to it, bake for another 5 minutes and test again.
Remove and Cool: Remove the pan from the oven using heat-resistant oven mitts. Let the cornbread rest for a few minutes, then loosen the edges with a butter knife. Transfer it to a cooling rack and allow it to cool for about 10 minutes before slicing.
Slice and Serve: Cut the cornbread into nine squares and serve warm. Enjoy it plain or with a little butter or maple syrup. It also pairs well with smoked brisket, pulled pork, barbecue chicken, baked beans, and other classic barbecue sides.