Bloom the yeast on the stove Combine the milk, water, sugar, and melted butter in a small saucepan. Heat over low heat, stirring occasionally, until the mixture reaches 110°F — warm to the touch but not hot. Remove from heat, stir in the yeast, and let sit for 5–7 minutes until a foamy head develops.
Mix the dry ingredients While the yeast blooms, whisk together the flour and salt in the bowl of a stand mixer fitted with a paddle attachment.
Combine and knead Beat the egg into the yeast mixture, then slowly pour the liquid into the flour with the mixer running on low. Once combined, increase to medium-high and mix for 7 minutes until the dough is smooth, elastic, and pulls away from the sides of the bowl. Don't be alarmed — this dough will be sticky and wet. That is completely normal and exactly what you want for that soft, airy texture.
First rise Transfer the dough to a lightly oiled bowl and cover with a clean kitchen towel. Place in a warm spot and let rise until doubled in size, about 1 hour.
Cut the muffins Turn the dough onto a lightly floured surface and gently pat it down to just under 1 inch thick. Line two baking sheets with parchment paper and dust generously with cornmeal or semolina. Use a 2½-inch round cutter to stamp out the muffins and transfer them to the prepared pans. Re-knead and re-roll the scraps and continue cutting until all the dough is used up.
Second rise Loosely cover the pans with a clean kitchen towel and let the muffins puff in a warm spot for 30 minutes.
Cook on the griddle Heat your griddle over low heat and dust the surface with cornmeal. Arrange as many muffins as will fit across the griddle. The key is low, controlled heat — this is what cooks the muffins all the way through without burning the outside. Cook for 6–8 minutes until the bottoms are golden brown and the tops look dry. Flip and cook another 6–8 minutes until browned on the other side. Clear off the old cornmeal between batches and add a fresh dusting each time. Cook a test muffin first to dial in your heat level.
Enjoy warm! To split, always use a fork to poke around the edge and pry open — this preserves those classic nooks and crannies.