In a large saucepan, bring potatoes and water to a boil. Reduce heat; cover and simmer for 15-20 minutes or until tender. Drain potatoes, reserving 1/2 cup cooking liquid; cool liquid to 110°-115°. Mash potatoes; set aside to cool to 110°-115°.
In a large bowl, dissolve yeast in warm milk. Add the mashed potatoes, cooking liquid, sugar, butter, salt, egg and 1-1/2 cups flour; beat until smooth. Stir in enough remaining flour to form a soft dough. Do not knead. Cover and let rise in a warm place until doubled, about 1 hour.
Punch dough down. Turn onto a lightly floured surface; divide into 24 pieces. Gently roll each into a 12-in. rope. Holding one end of rope, loosely wrap dough, forming a coil. Tuck end under; pinch to seal. Place 2 in. apart on greased baking sheets. Cover and let rise until doubled, about 30 minutes.
With thumb, make a 1-in. indentation in center of each coil. Fill with cherry pie filling. Bake at 400° for 12-15 minutes or until golden brown. Remove from pans to wire racks to cool. Drizzle with Vanilla Glaze.