In a mixing bowl, combine the active sourdough starter, warm milk, sugar, and salt. Mix well until blended.
Gradually add the all-purpose flour and bread flour to the mixture, stirring with a fork or whisk until it forms a rough dough.
Transfer the dough onto a floured surface and knead for about 5 minutes, or until the dough is smooth and elastic.
Place the dough into a lightly greased bowl. Cover it with a clean kitchen towel and let it rise at room temperature for 4-6 hours, or until doubled in size.
Once the dough has risen, turn it out onto a floured surface and flatten it gently. Using a bench scraper or round cutter, cut out 6 muffins, about 3 inches in diameter.
Place the cut muffins on a baking sheet lined with parchment paper. Dust the tops with cornmeal to prevent sticking. Cover with the towel and let them rise for another 30-60 minutes.
Heat a cast iron skillet or non-stick frying pan over medium-low heat. Carefully transfer the muffins to the skillet, making sure not to overcrowd the pan.
Cook the muffins for about 7-8 minutes on each side, or until they are golden brown and sound hollow when tapped.
Once cooked, transfer the muffins to a wire rack to cool completely before slicing.