Preheat oven to 400 F.
Combine corn meal, salt, baking powder, and baking soda in a large mixing bowl.
In a separate bowl, lightly whisk the eggs to break them, then whisk in the buttermilk.
Once the oven has reached temperature, put the butter in the skillet and place in the oven to melt and brown the butter. It should take about 5 minutes.
While the pan is in the oven, add the buttermilk mix to the cornmeal mix and stir just enough to combine. Add the cheese and peppers, stirring again just enough to combine.
Remove the pan from the oven, and pour in the batter. Return to the oven and bake until the top is golden and it passes the toothpick test, about 20 minutes.
Serve warm, cold, with a pat of butter, or even honey!