Preheat the oven to 425 degrees F; place three 12-cup mini muffin tins in the oven to heat up.
Meanwhile, you will need two bowls for the cornbread batter. In one bowl, whisk together the cornmeal, flour, sugar, salt and baking soda. In the other bowl, whisk together the eggs, buttermilk and melted butter. Pour the wet ingredients into the dry, and stir to combine.
Remove the muffin tins from the oven. With a 1-tablespoon scoop, carefully fill each cup half full with batter. Place a piece of hot dog in the center of each muffin cup, and dollop with 1/4 teaspoon relish.