Add the first 7 ingredients to a 1-1/2- or 2-pound bread machine according to the manufacturer's directions. Select dough cycle. When cycle is complete, remove dough from machine and divide into 4 portions. Cover and let rest for 10 minutes.
Shape 3 portions into 6 balls each, making a total of 18 balls; set aside.
Shape the remaining portion into 18 small balls. Place large balls of dough in greased 2-1/2-inch muffin pans or 3-inch fluted individual brioche pans. Press dough in the center. Brush with water. Press the small ball into indentation. Let rise in a warm place about 40 minutes or until nearly double.
Stir together egg and 1 tablespoon sugar; brush onto tops. Bake in a 375 degree F oven for 12 to 15 minutes or until golden. If desired, brush again with egg mixture after 10 minutes. Cool on a wire rack.