Heat the oil in 12-inch cast-iron skillet over high heat until very hot. Sprinkle the beef with salt and pepper and toss with 1 tablespoon of the flour and 1 tablespoon of the cornmeal. Add the beef to the skillet and cook, stirring occasionally, until the meat is browned, 6 to 10 minutes.
Reduce heat to medium. Add the onion and garlic and cook, stirring often, until onion is soft, about 8 minutes. Add the chili powder (use less if you like milder chili) and cumin and cook until fragrant, about 1 minute. Add the chicken stock, tomatoes, beans and 1 tablespoon of the sugar and bring to simmer. Cook until the meat becomes tender and the sauce has thickened, about 30 minutes. If the liquid reduces to less than three-quarters of the way up the sides of the meat, stir in a little water.
Meanwhile, position a rack in the center of the oven and preheat to 400 degrees F. Whisk the remaining 3/4 cup cornmeal, 3/4 cup flour, 3 tablespoons sugar, baking soda and 1 teaspoon salt together in a medium bowl. Whisk the sour cream, milk and egg together in another bowl. Add the wet ingredients to the dry ingredients, whisking until well combined. Stir in the melted butter and Cheddar cheese. Drop oval-shaped spoonfuls of batter on top of the chili, leaving space in between. The batter will not completely cover the chili.
Bake until the cornbread is golden brown and springs back when touched, and the chili is hot and bubbly, about 17 minutes. Remove the skillet from the oven and serve with more sour cream.
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