Add ingredients to bread machine pan in the order suggested by manufacturer. Select dough/manual cycle.
When cycle is complete, remove dough from machine to a lightly floured surface. Divide dough into 12 equal portions; form into smooth balls. Arrange balls in greased 9-inch round pan. Cover; let rise in warm, draft-free place until doubled in size, about 45 minutes. Brush with Egg Glaze.
Bake at 350°F for 25 to 30 minutes or until done. Remove from pan; cool on wire rack.
*In place of mashed potatoes and potato water, use 1/3 cup instant mashed potatoes and 3/4 cup water.