Preheat the oven to 425°F and line a baking tray or sheet pan with foil. Lightly grease the foil if needed to prevent sticking.

In a medium bowl, stir together the self-rising cornmeal mix, buttermilk, and melted butter until a thick, scoopable batter forms. Do not overmix; just combine until no dry pockets remain.

Drop the batter by small spoonfuls onto the prepared tray, spacing them slightly apart. Gently flatten each one into a small round.

Bake for 10 to 14 minutes, or until the pennies are golden brown around the edges and set in the center. If desired, bake an additional 1 to 2 minutes for crisp edges.

Remove from the oven and brush lightly with any remaining melted butter if you like.

Serve warm, or let them cool slightly so the edges stay crisp.