In the bowl of a stand mixer fitted with the dough hook, combine the warm milk, butter, flour, starter, and optional yeast. Hold the salt back for now. Mix on low speed until a rough but cohesive dough forms.

Add the salt and mix on medium-high speed until a smooth dough forms, about 6 minutes.

Transfer the dough to a lightly oiled large bowl, cover with plastic wrap, and bulk proof in a warm spot for 30 to 40 minutes.

Flip the dough over and degas by folding the edges in and pressing down, or simply pressing down all over. Cover and return to the warm spot until doubled, about 30 to 40 minutes more.

Turn the dough out onto a smooth, unfloured work surface. Degas and press the dough out with your fingers into a circle about 1/4 inch thick.

Cut out 2 1/2 inch rounds using a biscuit cutter or round cookie cutter. Place cut-side down on a cornmeal-dusted half-sheet pan.

For scrap dough, knead the pieces together, cover, and bulk proof for an additional hour before pressing and cutting again.

Cover the pan loosely with plastic wrap and final proof for 45 minutes to 1 hour, until visibly puffed and doubled in height. Dough made without added yeast will need longer.

Meanwhile, preheat the oven to 350°F (no fan) and set a wire rack inside a rimmed baking sheet.

Heat a large skillet over medium heat with about 1 teaspoon vegetable oil and 1 1/2 teaspoons butter until warm but not smoking. If the butter browns before you add the muffins, the pan is too hot.

Add the muffins cornmeal-side down and cook until golden brown, about 1 1/2 to 2 minutes per side. Transfer to the rack-lined baking sheet. Wipe out the pan between batches.

Bake for 10 minutes. Cool on the rack and serve toasted.