Whisk the yeast into the warm milk in the bowl of a stand mixer fitted with the dough hook. Let bloom for about 10 minutes, until bubbles float to the surface.
Add the flour and butter. Mix on low speed until a rough dough forms.
Add the salt. Mix on medium-high until the dough is smooth and passes the windowpane test (a small piece stretches thin without tearing).
Transfer dough to a lightly oiled bowl, cover with plastic wrap, and bulk proof in a warm spot for about 1 ½ hours. After 30 minutes, flip and degas the dough, then cover and continue proofing until doubled.
Generously sprinkle cornmeal onto a parchment-lined sheet pan and set aside.
Turn the doubled dough onto a clean, unfloured countertop. Press and spread it out with your fingers to approximately ¼ inch thick. Cut rounds using a 3-inch biscuit cutter or cookie cutter and place them cornmeal-side down on the prepared pan.
Knead the remaining dough scraps together, return to the oiled bowl, cover, and proof for 30 minutes. Then repeat step
Cover the sheet pan with plastic wrap and final proof the cut muffins for 45 minutes to 1 hour, until visibly puffed and doubled in height.
Preheat the oven to 350°F conventional. Place a wire rack inside a rimmed baking sheet and set aside.
Heat a large sauté pan over medium heat with about 1 teaspoon vegetable oil and 1 ½ teaspoons butter until warm but not smoking. Add muffins cornmeal-side down and cook about 1 ½ minutes per side, until golden brown. Transfer to the rack.
Wipe out the pan between batches to maintain even color.
Bake on the rack-lined pan for 10 minutes. Cool on a rack before splitting and serving.