Preheat the oven to 400 degrees F. Spray a 12 cup muffin pan with nonstick spray.
In a medium saute pan, over medium heat, add 2 tablespoons butter. Once the butter has melted add the onions and the peppers and saute until soft, about 4 minutes. Season with salt, to taste. Stir in the corn and cook until heated through. Set aside to cool.
Melt the remanding butter in a small pan over low heat and once melted, remove from the heat.
In a large bowl, combine the flour, cornmeal, baking powder, baking soda and salt.
In another large bowl, add the buttermilk and the eggs. Whisk lightly until combined. Using the well method, add the liquid ingredients to the dry ingredients and fold together until combined. Add the sauteed vegetables with the melted butter and the shredded cheese and continue to fold. The batter will be very thick.
Using a 1/2 cup measure, evenly scoop the batter into the muffin tin. Bake for 10 minutes. Remove from the oven and let cool for 10 minutes on a wire rack before serving.