In the bowl of a stand mixer fitted with the paddle attachment, combine the flour, sugar, salt and yeast. Mix in the butter (or shortening) and 3/4 cup of milk (or buttermilk). If the dry ingredients are not yet fully incorporated, add enough of the remaining milk so a dough forms. Stop mixing right when this occurs: don’t over mix! Sprinkle flour on a dry surface and turn the dough out of the mixer, and knead by hand for about 9-10 minutes. The dough should be tacky (but not sticky), and register 77 to 81 F. Transfer to a lightly oiled bowl and roll the ball of dough around the bowl to coat. Cover with plastic wrap and let rise for at least an hour, or until the dough doubles in size. It helps to keep the dough (in terms of rising) in a relatively warm place–away from cold, drafty windows or open doors.
Divide the dough into 6 equal pieces and shape into small balls. Lay parchment paper on a baking sheet and spray lightly with oil. Sprinkle with cornmeal.
Move the dough balls to the baking sheet, spacing them evenly with enough room to rise and double in size. Mist them lightly with oil and sprinkle with cornmeal then cover the pan loosely with plastic wrap and allow to rise another hour, or until the rolls are nearly double in size. Preheat the oven to 350 F. Heat a flat griddle to medium (350 F) (you can also use a skillet on the stove top if you don’t have a griddle). Brush the griddle lightly with oil and gently transfer the dough balls to the griddle. Allow them to cook for 5-8 minutes or until the bottoms are a rich golden brown color. Be careful not to burn. Carefully flip and cook the other side for the same amount of time. They should flatten as they cook.
Remove the muffins from the skillet and transfer them to a parchment or Silpat-lined baking sheet. Bake in the preheated oven for 6-8 minutes.Transfer the baked muffins to a cooling rack and let cool at least 30 minutes before slicing or serving.