Place milk in the bowl of your stand mixer fitted with the paddle attachment and sprinkle yeast over top. Let sit for 10 minutes to activate and then add the butter, salt, sugar, egg, and flour.
Mix on low until the flour is incorporated and then switch to medium and beat for 5 minutes. The dough will be very soft and sticky.
Oil a large bowl and then scrape dough out into it, cover, and let rise for about 2 hours.
Oil your hands (to prevent the dough from sticking) pinch pieces of dough off (2 oz, if you have a kitchen scale or about the size of the center of your palm), form a ball, and place on a (cooled) griddle pan or in a large saute pan that is generously dusted with cornmeal.
Put the remainder on a baking sheet dusted with cornmeal, or if you have another large saute pan, prep a second pan.
Let rest for 20 minutes.
Turn burner to medium low and cook until golden brown, about 10 -12 minutes on the first side and 8-10 min on the second side. (If they brown too quickly, reduce the heat.)
Heat 2nd pan and cook or carefully transfer the rest from the baking sheet so as not to deflate them and cook until done.
Let cool completely on a rack before splitting open with a fork.
Muffins will keep fresh on the counter a few days and freeze well.