Preheat oven to 350°F (175°C).

In a large mixing bowl, whisk together the yellow cornmeal, all-purpose flour, sugar, salt, baking powder, and baking soda.

In a separate bowl, whisk the beaten eggs, buttermilk, and vegetable oil.

Add the wet ingredients to the dry ingredients and stir until just moistened.

Gently fold in the cream-style corn, chopped onion, chopped green pepper, and shredded Cheddar cheese.

Pour the batter into a greased 9-inch square baking pan or a 10-inch heavy skillet.

Bake for 30-35 minutes, or until a wooden skewer inserted into the center comes out clean and the cornbread is golden brown.

Let cool slightly before slicing and serving.