Preheat your oven to 400°F (200°C). Grease a 9-inch square baking dish or cast-iron skillet.
In a large mixing bowl, combine the cornmeal, flour, baking powder, salt, and sugar (if using). Stir until well mixed.
In a separate bowl, whisk together the buttermilk, eggs, and melted butter.
Pour the wet ingredients into the dry ingredients and stir until just combined. Be careful not to overmix; a few lumps are okay.
Fold in the shredded cheddar cheese and diced jalapenos, distributing them evenly throughout the batter.
Pour the batter into the greased baking dish or skillet and spread it out evenly.
Bake in the preheated oven for about 20-25 minutes, or until the top is golden brown and a toothpick inserted into the center comes out clean.
Remove from the oven and let the cornbread cool for a few minutes before cutting it into squares or wedges. Serve warm.