Preheat the oven to 400°F (200°C).
In a mixing bowl, combine the cornmeal, flour, sugar, baking powder, and salt. Mix well.
In a separate bowl, whisk together the milk, eggs, and vegetable oil until well combined.
Pour the wet ingredients into the dry ingredients and stir until just combined. Be careful not to overmix.
Gently fold in the diced jalapeños and shredded cheddar cheese (if using).
Grease your baking dish (8x8 inch) with cooking spray or a small amount of oil.
Pour the batter into the greased baking dish and spread it evenly.
Bake in the preheated oven for about 25 minutes, or until the top is golden brown and a toothpick inserted into the center comes out clean.
Let cool for a few minutes before slicing into squares and serving.