Mix warm water with sugar in a large mixing bowl until the sugar has dissolved. Sprinkle yeast over the surface of the water, and let stand until the yeast begins to form a creamy layer on the water. Stir the yeast into the water. Stir in salt, and 1 cup of bread flour, and beat the flour in to form a loose batter. Stir in 1 more cup of flour, and mix in the mozzarella cheese, milk, and basil. Mix in the remaining 2 cups of flour in 1/2-cup additions.