Preheat the oven to 400°F (200°C).
In a large mixing bowl, combine cornmeal, flour, baking powder, and salt.
In a separate bowl, whisk together buttermilk, vegetable oil, and egg.
Pour the wet ingredients into the dry ingredients and stir until just combined.
Fold in the shredded cheddar cheese and diced jalapeños.
Grease a baking pan or skillet and pour the batter into it, spreading evenly.
Bake for 20-25 minutes, or until a toothpick inserted comes out clean.
Allow to cool for a few minutes before slicing and serving.