In a large mixing bowl, combine the sugar, yeast and warm water. Allow to stand for 5 minutes.
Add the salt, milk, vegetable oil, 2 cups of the flour and mix with a wooden spoon until fairly smooth.
Add the remaining flour and blend until all is incorporated. Scrape the sides of the bowl down and cover with plastic. The dough should double in size after about 1 hour.
Place the dough on a well floured surface and knead 2 to 3 times.
Press the dough into a square about 1/2 inch thick.
Using a 3 inch round cup or biscuit cutter to cut out the muffins.
Place the muffins on a baking sheet that is lightly dusted with the corn meal. Sprinkle the corn meal over the muffins to coat.
Cover the muffins with plastic and allow to rise again for 30 minutes.
Heat a skillet over med/low heat and add about 1/4 tbsp of the oil to coat the pan.
Cook the muffins, a few at a time for about 5 minutes on each side. They should be golden brown on the outside and puffy in the middle.
Allow the muffins to cool. Open the muffins with a fork when you're ready to use them.
Toast the split muffins in a toaster until the middle is golden brown.