Place a pizza stone in the oven. Preheat the oven and stone to 450 degrees for at least 30-45 minutes.Divide the dough into two pieces. Flour the counter, and roll one piece of the dough out to about 12 inch diameter.Roll two sides up to oppose each other, creating a football shape with a large well in the center. Pinch the edges on either side together. Repeat with the other piece of dough.Divide the cheese evenly between the two pieces of dough, filling the centers of each.Crack each egg into its own small bowl. Set aside.Using a large spatula or cutting board, carefully transfer each piece of dough directly onto the pizza stone.Bake for about 12-13 minutes, until the dough browns and the cheese becomes bubbly. Make a small well in the cheese, and carefully pour one egg into the well. Repeat with the other piece of dough.Bake for another 2-4 minutes, until the white is almost completely set.Remove from the oven. Serve, preferably with a crisp, green salad with a light vinaigrette.