Preheat your oven to 400°F (200°C).
In a large bowl, mix cornmeal, flour, baking powder, and salt.
In a separate bowl, whisk together buttermilk, vegetable oil, and eggs.
Pour the wet ingredients into the dry ingredients and stir until just combined.
Fold in corn kernels, jalapeños, and cheese.
Grease a baking dish or cast-iron skillet.
Pour the batter into the prepared dish.
Bake for 25-30 minutes until golden brown and a toothpick comes out clean.
Let it cool for a few minutes before slicing.
Serve warm and enjoy!