Khachapuri (Georgian Cheese Bread)

Name: Khachapuri (Georgian Cheese Bread)
Ingredients: 3 tablespoons (43g) unsalted butter; 1 cup (227g) milk; 1 1/2 teaspoons granulated sugar or 1 tablespoon non-diastatic malt powde; 1/2 teaspoon coriander; 1 1/2 teaspoons (9g) salt; 2 teaspoons instant yeast or; 2 3/4 cups (330g) King Arthur Unbleached Bread Flour; 2 cups (227g) shredded mozzarella or Muenster cheese; 1/2 cup (113g) ricotta cheese; 1/2 cup (57g) crumbled feta cheese; 1 large egg; 2 tablespoons (14g) King Arthur Unbleached Bread Flour; 1/2 teaspoon salt; 1/2 to 1 teaspoon coarsely ground pepper; 2 tablespoons coarsely chopped flat-leaf parsley; 2 tablespoons finely chopped chives; 1 large egg beaten with 1 teaspoon water; 4 large eggs cold from the refrigerator; 4 teaspoons (19g) butter