In a large bowl, mix the starter, milk, honey, and salt. Add the flour and melted butter, and stir into a shaggy dough. Knead briefly in the bowl until no dry spots remain.

Transfer to an oiled bowl, cover, and refrigerate for 8 to 12 hours.

Turn the dough onto a floured surface and pat it ¾ inch thick. Cut 8 rounds, dust both sides with cornmeal, and place on a cornmeal-dusted baking sheet.

Cover with a towel and proof at room temperature for 45 to 60 minutes, until slightly puffed.

Preheat a griddle or skillet over medium-low heat. Butter lightly, then cook muffins in batches, 6 to 8 minutes per side, until deep golden and cooked through.

Cool on a rack for 5 minutes, then fork-split each muffin, toast, and serve warm.