Mix the Dough: In a large bowl, stir together the sourdough starter, lukewarm milk, sugar, and melted butter until smooth. Add the flour and salt, mixing until a shaggy, sticky dough forms. Knead by hand (or in a stand mixer with a dough hook) for 2–3 minutes until the dough comes together—it should feel soft and slightly tacky.
First Rise: Cover the bowl with a damp towel or plastic wrap. Let rise at room temperature (70–75°F) for 4–6 hours, until puffy and nearly doubled. For an overnight option, refrigerate after 2 hours and let it rest until the next day.
Shape the Muffins: Turn the dough onto a lightly floured surface. Divide into 8 equal pieces (90–100g each). Roll into balls, then flatten into discs about 3½ inches wide and ¾-inch thick. Dust generously with cornmeal (or semolina/rice flour). Place on parchment, cover loosely, and let rise for 1–2 hours until puffy. You can also roll the dough and cut rounds with a biscuit cutter.
Cook the Muffins: Heat a cast iron skillet (or heavy griddle) over medium-low. Cook 3–4 muffins at a time, 5–7 minutes per side, until golden brown and cooked through (internal temp 200°F). Adjust heat if browning too quickly.
Split and Serve: Once slightly cooled, split muffins with a fork (not a knife) to get those classic “nooks and crannies.” Toast and serve with butter, jam, or your favorite toppings.