Combine first 6 ingredients in the bowl of a stand mixer fitted with a bread hook; mix a bit. Heat milk and 2 tablespoons butter in a small saucepan to between 120°-130°. Add milk mixture to flour mixture; mix on medium speed. Add water and eggs; mix well until dough forms a ball. Fold in 3 ounces of shredded cheese.
Place ball of dough in a oiled bowl. Allow to rise in a warm space, free of drafts for 1 hour.