Since you cook these on top of the stove, there is no need to preheat the oven.Proof the yeast in the l/2 Cup of lukewarm milk with the sugar.Scald the 1 cup of milk, melt the butter in it and let cool to lukewarm.
Add the salt and the slightly beaten egg to the milk-and-butter mixture. Pour the yeast sponge into a large mixing bowl and blend in the milk-butter-and-egg mixture. Add the flour, a little at a time,mixing together well.
Turn the dough out onto a lightly floured work surface and knead, adding more flour if necessary.
Knead until elastic and shiny.
Then place the dough in a large buttered bowl, cover with a towel and let rise for at least 1 hour, until doubled in bulk.
Meanwhile, pour the cornmeal onto a platter and set aside. Take the dough out onto the work surface and knead again for a couple of minutes.
Roll it out with a rolling pin to a thickness of about 1/3" and, with a glass or a large biscuit cutter, cut out round cakes.
Put these onto the platter with the cornmeal, press down slightly and turn to get the other side covered with cornmeal.
Place on a baking sheet and cover with a towel.
Let stand for about 20 to 30 minutes or until doubled in size. Place a skillet over medium heat and when hot, brush with a little melted butter, turn the heat low and place about 5 to 6 muffins in the pan.
Cook for approximately 5 minutes on each side, or until they are slightly brown.
Cool on a rack.
Toast after they are completely cooled off and right before serving them.