Bring milk to a boil in a large sauce-pan over medium heat; stir in grits, and cook, stirring often, 5 minutes (mixture will be very thick).
Remove from heat; add salt and cheese, stirring until cheese is melted.
Let stand 25 minutes, stirring occasionally.
Combine 1 cup warm water, sugar, and yeast in the mixing bowl of a heavy-duty stand mixer; let stand 5 minutes.
Add grits mixture, beating at medium-low speed with the dough hook attachment until well blended.
Add 4 cups flour, 1 cup at a time, beating until blended after each addition and stopping to scrape down sides as necessary. Gradually add enough flour to make a stiff but slightly sticky dough. Dough will form a ball around mixer attachment.
Shape dough into a ball with well-floured hands, and place in a well- greased bowl, turning to coat top. Cover and let rise in a warm place (85), free from drafts, 1 hour or until doubled in bulk.
Punch dough down, and divide into thirds; roll each third into a 14- x 9-inch rectangle on a lightly floured surface.
Spread basil pesto evenly over each dough rectangle; sprinkle each with mozzarella or crumbled goat cheese.
Roll up, jelly-roll fashion, starting with each short side and ending at middle of dough; form 2 rolls per loaf.
Place into lightly greased 9- x 5-inch loafpans; cover and let rise in a warm place (85), free from drafts, 45 minutes or until doubled in bulk.
Bake at 350 for 35 to 40 minutes or until golden.
Let bread cool in pans on wire racks 10 minutes.
Remove from pans, and cool completely on wire racks.
Note: For testing purposes only, we used Cracker Barrel Vermont Sharp White Cheddar.
