Make the dough starter by mixing the flour, water, and yeast in a small bowl. Whisk until the batter is smooth and glossy, about 100 strokes. Cover and set aside for 1 to 12 hours. The longer you let it ferment, the better the flavor.
In the bowl of a stand mixer or large mixing bowl, combine the milk and the yeast for the dough. Add the starter and use a whisk to break it up and dissolve it into the milk. Mix well until quite frothy.
Add the sugar, butter, and salt to the bowl. Whisk to combine. Add 3 cups of the flour and mix with a sturdy spatula until you form a shaggy dough.
With a dough hook on a stand mixer, knead the dough until it comes together in a ball, 5 to 8 minutes on medium speed. You can also knead by hand if you don't have a mixer. Only add flour a little bit at a time if the dough is extra sticky. The dough is ready when it forms into a ball and springs back when poked; it will feel tacky to the touch, but shouldn't stick to your hands.
Transfer the dough to a large, lightly-oiled bowl. Cover and refrigerate overnight, or up to 3 days.
Turn the risen dough out onto work surface that's lightly floured. Divide the dough into 12 equal pieces and roll into balls.
Sprinkle semolina or cornmeal over a baking sheet and arrange the balls on top. Allow a little bit of room between each ball of dough. If you have muffin rings, place them around the balls. Sprinkle the tops of the balls with more semolina or cornmeal. Let the dough rise until puffy, 1 to 2 hours.
Warm a skillet, preferably cast iron, over medium low heat. Place another rimmed baking sheet in the center of oven and preheat to 350°F. Coat the bottom of the skillet lightly with a small pat of butter to prevent sticking. Working in small batches to avoid crowding, and keeping remaining dough covered, cook the muffins 6 to 8 minutes per side until deep golden brown. Transfer muffins using a spatula to preheated baking sheet in oven and bake the muffins until cooked through, 5 to 10 minutes.
Let the muffins cool on a wire rack for at least 30 minutes, then split with a fork, add your favorite spread or topping, and enjoy! The muffins will keep for several days in an airtight container, or they can be tightly wrapped and frozen for up to 3 months.