Put a 10-inch cast iron skillet over medium-high heat and add the oil. When the oil is hot, add the onions and cook until they are soft and beginning to brown, about 5 minutes. Remove the onions from the pan onto a plate. Leave the remaining oil in the pan.
In a large bowl, whisk together the baking mix, cornmeal, sugar, baking soda, salt, and cayenne. In another bowl, whisk together the eggs and milk. Add the wet ingredients to the dry ingredients and stir until combined. Fold in the reserved onions and the jalapeno. Pour the batter into the skillet the onions were cooked in and bake until a toothpick inserted in the center comes out clean, 20 to 25 minutes. (Reserve 2 pieces cornbread for the Online Round 2 Recipe Pork and Cornbread Bites.)