Heat oven to 350°F. Grease a 2-quart baking dish or a 9-inch square pan.
Whisk the eggs in a large bowl. Stir in sour cream and melted butter until smooth.
Fold in the creamed corn and the drained sweet corn.
Sprinkle in the corn muffin mix and gently mix just until combined; do not overmix.
Stir in half the cheddar, then season with the salt and black pepper.
Spread the batter into the prepared dish and scatter the remaining cheese over the top.
Bake until puffed, set in the center, and golden at the edges, 48–55 minutes. Rest 10 minutes before serving.