In a saucepan, heat milk, butter, salt and sugar to lukewarm.
Add 4 cups of cheese gradually and stir until cheese and butter are melted.
Pour into a large bowl and when lukewarm, add yeast mixture and 2 cups semolina flour.
Work the mixture with a wire whisk until smooth then add caraway seeds and dry mustard.
Mix.
Batter will begin to thicken and take on a grainy look.
Add 1/2 cup of cheese.
Mix.
Add 3 cups bread flour, gradually, stirring with a wooden spoon.
Dough will be sticky.
Turn out on a floured surface and knead until smooth and elastic, gradually adding remaining 2 cups of flour.
If you want to make a braided loaf, shape the dough into 3 balls of equal size and roll out each ball into an 8-inch-by-12-inch rectangle with rolling pin.
Starting two inches from the top, slice each rectangle into three equal-size strips.
Loosely braid the strips on each rectangle.
Pinch the braided ends and form a circle with each piece of dough by connecting it with the other end.
This will yield three rings.
(If you want a nonbraided ring, simply roll out the three equal-size dough balls into loaves in the shape of French bread, and make a ring.)
Make slashes on top of the ring with a sharp knife.
Place dough rings on baking sheets dusted with cornmeal and let them rise until doubled.
Bake at 350 degrees for one hour, until a hollow sound is heard when the bottom is tapped.