In a large mixing bowl, combine the sourdough starter, warm milk, and sugar. Stir until well mixed.

Add the flour and salt, and mix until a shaggy dough forms. Stir in the melted butter and knead the dough on a floured surface for about 5-7 minutes, until smooth and elastic.

Place the dough in a greased bowl, cover with a clean kitchen towel, and let it rest at room temperature for 6-8 hours (or overnight) until doubled in size.

Turn the dough onto a lightly floured surface and roll it out to about ½ inch thick. Use a round cutter (3-4 inches in diameter) to cut out muffin shapes. Place them on a baking sheet dusted with cornmeal. Sprinkle more cornmeal on top, cover, and let them rise for 1-2 hours.

Heat a skillet or griddle over low heat and lightly grease it. Cook the muffins for 6-8 minutes per side, until golden brown and cooked through. If they brown too quickly, reduce the heat to avoid undercooking the inside.

Transfer the muffins to a wire rack to cool completely. Split with a fork before toasting for the best texture.