Heat the oil in a stockpot over medium heat. Add the cut pumpkin, onion, jalapeños, garlic, chili powder, cumin, black pepper, and two thirds of the salt. Cook until the vegetables start to soften, 5 to 7 minutes. (The pumpkin should be slightly soft around the edges, but probably won't be cooked through yet.)

Add the ground beef, breaking it up with a stiff spatula, and continue to cook until no longer raw, 3 to 5 minutes more. Add the black beans, diced tomatoes, beer, and the rest of the salt to the pot.

Bring the soup to a boil. Reduce to a simmer and cook uncovered, stirring occasionally, until the pumpkin has cooked through and the flavors have had time to mingle, about 30 minutes.

Taste and add more salt or spices if needed. (If the chili tastes a little bland, add more spices; if the chili tastes a little bitter, add more salt.)

Mix and Bake the Cornbread: Melt the butter for the cornbread. In a large bowl measure out and add the flour, cornmeal, sugar, baking powder, and salt. Whisk to combine well. To the dry mix, add in the melted butter then measure out and add in the milk a little at a time while stirring. Stir until combined. Add more milk as needed to make a batter consistency, not too thick and not too watery.

Lightly grease an appropriately sized oven-safe container with non-stick spray. Evenly scoop the batter into the greased container and place it in the oven. Bake for about 15 - 20 minutes.

Finish the Cornbread: Check that the cornbread is done by inserting a toothpick in the center. If it comes out clean, the cornbread is done. Remove from the oven and let cool. If the toothpick has wet batter stuck to it, more cooking time is required. Cook a few minutes longer, then test again. Let cool for about 10 minutes before serving.

Serve the chili with cornbread and pumpkin beer.