Combine warm milk, warm water, sugar, and yeast in a large bowl. Stir gently and leave 5–10 minutes until foamy. If no foam forms, start over with fresh yeast.
Add softened butter, beaten egg, and salt to the yeast mixture. Add flour one cup at a time, stirring between additions. Turn onto a lightly floured surface and knead 8 minutes until smooth and elastic. Dough should be soft and slightly tacky — do not add too much extra flour.
Place dough in a lightly oiled bowl, cover tightly with plastic wrap, and leave at room temperature for 1 hour until doubled.
Punch dough down, re-cover, and refrigerate for at least 8 hours or overnight. This cold fermentation develops flavor and makes the dough easier to handle.
Remove dough from fridge and rest at room temperature 20–30 minutes. Roll to 3/4 inch thickness on a lightly floured surface. Cut rounds using a 3.5–4 inch cutter. Place on a cornmeal-dusted tray and dust tops generously with cornmeal. Cover and rest 30–45 minutes until slightly puffed.
Heat a cast iron skillet or griddle over the lowest heat. Lightly grease with butter or oil. Cook muffins 7–8 minutes per side until golden-brown on both sides and hollow-sounding when tapped. Do not rush with high heat — the inside needs time to cook through.
Cool 5 minutes. Split with a fork around the equator for maximum nooks. Toast and serve with butter, jam, or eggs.
