In a large bowl, add the all-purpose flour, cornmeal, sugar, baking powder, salt and baking soda and whisk until combined.
In a medium bowl add the melted butter, buttermilk, eggs and whisk until combined.
Add the wet ingredients to the dry and mix until incorporated.
Mix in the jalapenos, cheese, and corn.
Heat a 10-inch skillet on medium-high heat and add 2 tablespoons of butter let it melt and begin to sizzle. Turn off the heat and add the cornbread batter into the skillet (it's ok if the butter raises to the top of the batter on the edges.). Add slices of jalapenos if you prefer, and a sprinkle of shredded cheese.
Bake for 20-25 minutes or until golden brown and a toothpick comes out clean.
let cool 5 minutes then cut into slices.
Notes
You can make your own buttermilk by adding 1 tablespoon lemon juice or white vinegar to the whole milk. Let it sit for 10 minutes and stir.
An 9x9 baking pan will also work just butter the bottom of the pan before adding the batter.