Preheat your oven to 400°F (200°C). Place a 10-inch cast iron skillet or an 8x8 inch baking dish in the oven while it preheats to get it hot.

In a large bowl, whisk together the flour, cornmeal, sugar, baking powder, and salt.

In a separate medium bowl, whisk together the milk, melted butter, and eggs until well combined.

Pour the wet ingredients into the dry ingredients and stir until just combined. Do not overmix; a few lumps are okay. Fold in the diced jalapeño and shredded cheddar cheese.

Carefully remove the hot skillet from the oven. Add a tablespoon of butter or oil to the hot skillet and swirl to coat. Pour the cornbread batter into the hot skillet and spread evenly. Bake for 25-30 minutes, or until golden brown and a wooden skewer inserted into the center comes out clean.

Remove the cornbread from the oven and let it cool in the skillet for a few minutes before slicing and serving. It's delicious warm with a pat of butter.