Preheat the oven to 400°F. Place a large cast-iron skillet in the oven while it preheats.
Mix the batter: Combine the muffin mix, eggs, milk, mashed sweet potato, and sour cream in a large bowl. Melt half of the butter (¼ cup) in the microwave. Add the melted butter to the mixture in the bowl and stir just until the ingredients are combined and moistened.
Remove the hot skillet from the oven. Cut the remaining ¼ cup butter into slices and add to the skillet. Let the butter melt and tilt the pan to coat the bottom with melted butter.
Pour the batter into the hot skillet and spread to an even layer. Bake for 22 minutes or until a toothpick inserted in the center comes out clean.
Let the cornbread cool for about 5 to 15 minutes. Cut into wedges and serve.