Incorporate the sourdough starter, sugar, and milk. Flour and salt in a large bowl. Allow the mixture to stand covered for 30-60 minutes.
Knead the dough for 5 minutes using a stand mixer with a dough hook on the lowest speed or by hand on a floured surface.
Transfer the kneaded dough to a greased bowl, cover, and let it ferment at room temperature for 8-12 hours.
After fermentation, form the dough into a smooth ball on a floured surface.
Cut the dough into 10 equal parts.
Roll each portion into a ball and slightly flatten.
Coat each side of the dough in cornmeal and set aside for 15 minutes.
Prepare a cast iron skillet over low heat. Arrange muffins in the skillet, with 2" spacing. Cover and cook the first side for four minutes. Flip the muffins and continue cooking for an additional four minutes.