Preheat oven to 400° F.
Put a 10-inch cast iron skillet in the oven while it preheats.
In a medium bowl, whisk together the cornmeal, flour, salt, baking powder, and baking soda. In a small bowl, whisk together the buttermilk and eggs.
Melt two tablespoons of the butter in a microwave-safe bowl.
When the oven is preheated (at least 10 minutes), whisk the buttermilk mixture into the dry mix until it is well combined.
Whisk in the two tablespoons of melted butter.
Remove the hot skillet from the oven and add the remaining two tablespoons of butter. The butter should melt and sizzle.
Use a spatula to distribute the butter evenly over the skillet. Once the butter is melted, pour in the cornmeal batter.
Using a spoon, add dollops of the Pepper & Onion Relish to the cornmeal batter and swirl it in. Use about a half cup (or half a jar) of the relish.
Bake the cornbread for 20 to 25 minutes, until it is golden brown around the edges and a tester comes out clean from the center.
Let the cornbread cool slightly before slicing and serving.