Whisk yeast, sugar, and 1 cup warm water in the bowl of a stand mixer fitted with the dough hook. Let sit until foamy.
Add warm buttermilk, butter, oil, salt, and 3½ cups flour and beat on low for 1 minute. It the dough looks too sloppy, add the remaining ½ cup of flour. Scrape down the bowl and mix on medium for 4-5 more minutes. Make sure not to overmix. The dough will be very wet and sticky but start to look like a dough (not a batter) but not like bread dough.
For best results, cover tightly and leave the dough in the refrigerator overnight to proof. The dough will be easier to work with if you can. If not, it will just take a little more work to get it into shape.
Cut 12 large squares of parchment (to rest your muffins on) and place them on 2 baking sheets. Dust generously with cornmeal (or alternatively you can spray the crap out of the parchment so it does not stick). Spray a clean work surface with nonstick spray, turn out dough, then spray bench scrape (or whatever you will use to portion the dough). Divide dough into 12 equal pieces and form each of the pieces into ball shapes, using a bench scraper to transfer dough to a baking sheet. Evenly space the muffins.
Sprinkle each piece with cornmeal or spray generously with oil. Cover with plastic wrap and allow to rice for 60-80 minutes (or until doubled in size).
Heat a large skillet or griddle over low.
Place another rimmed baking sheet in the center of the oven and preheat to 350°.
Attempt to slide your muffins off the parchment and onto the griddle/pan. If they will not budge, set parchment square on your pan and allow the dough to cook for a minute or two before you attempt to remove it.
Cook until bottoms are dark golden brown, 5–7 minutes. Turn and cook until the other side is dark golden brown, 5–7 minutes. Using spatula, transfer muffins to a preheated sheet in the oven and bake until cooked through and sides are dry to the touch but still spring back, 5–10 minutes.
Let muffins cool at least 30 minutes on a wire rack before splitting with a fork and serving.