Coat a 9-inch baking pan generously with butter and place it in a preheated 400°F oven to get hot.
2
In a bowl, combine all dry ingredients: fine cornmeal, self-rising flour, baking powder, baking soda, and kosher salt. Mix thoroughly.
3
In another bowl, beat the eggs, then add the buttermilk and melted butter, stirring well to combine.
4
Pour the wet ingredients into the dry mixture and stir until just combined, being careful not to overmix.
5
Gently fold in the cheddar cheese and finely minced jalapeño peppers.
6
Remove the hot pan from the oven and carefully pour in the batter. Using a spatula, spread it evenly and smooth the top.
7
Bake at 400°F for 25 to 30 minutes until the top is golden brown. If it needs more color toward the end, broil for about 2 minutes.
8
Remove the cornbread from the oven and run a small spatula around the edges to loosen it. Flip onto a cooling rack and let it rest briefly to allow steam to escape.
9
While the cornbread is still warm but not piping hot, generously brush the top with butter. Allow it to cool for 15 to 20 minutes before slicing.
10
Cut into squares and serve warm, adding more butter as desired.