Prepare the Oven and Muffin Pan: Preheat the oven to 375°F (190°C). Grease a 12-cup muffin pan or line it with paper liners to prevent the muffins from sticking.
Mix the Dry Ingredients: In a large bowl, whisk together the cornmeal, flour, baking powder, baking soda, salt, and sugar. Break up any lumps to distribute the leavening ingredients evenly.
Combine the Wet Ingredients: In a separate bowl, whisk the eggs, buttermilk, and vegetable oil until smooth. Make sure the eggs are fully incorporated into the mixture.
Prepare the Add-Ins: Stir together the shredded cheddar cheese, corn kernels, diced jalapeños, and chopped red bell pepper. Pat thawed or canned corn dry before using to avoid adding excess moisture.
Make the Batter: Pour the wet ingredients into the dry ingredients and stir gently until just combined. Fold in the cheese and vegetable mixture, taking care not to overmix the batter.
Fill the Muffin Cups: Divide the batter evenly among the 12 muffin cups, filling each about three-quarters full. Sprinkle a little extra cheddar cheese on top if desired.
Bake Until Golden: Bake for 18–22 minutes, or until the tops are lightly golden and a toothpick inserted into the center comes out clean. Allow the muffins a few extra minutes if the centers still look wet.
Cool and Serve: Let the muffins rest in the pan for 5 minutes before transferring them to a wire rack. Serve warm, when the cheese is still soft and the edges are lightly crisp.