Stir together 2 cups warm water and yeast in a large mixing bowl of a heavy-duty electric stand mixer until dissolved. Let stand 5 minutes.
Add potatoes, sugar, and butter to yeast mixture; beat at medium speed, using dough hook attachment, until blended. Add 7 cups flour and salt; beat at low speed 2 minutes. Add Caramelized Onions, and beat at medium speed 5 minutes. (Dough will be very sticky.) Sprinkle dough with remaining 1 tablespoon flour, and remove from bowl.
Shape into a ball, and place in a lightly greased bowl, turning to grease top. Turn off oven. Cover bowl with plastic wrap, and let rise in oven 30 minutes or until doubled in bulk.
Remove from oven. Remove and discard plastic wrap. Punch dough down, and turn out onto a lightly floured surface. Divide into 21 portions.
Shape each portion into a ball with floured hands. Place no more than 8 balls on each parchment paper-lined baking sheet. Cover with plastic wrap, and let rise again in a warm place, free from drafts, for 15 to 20 minutes or until doubled in bulk. Brush with egg and sprinkle with poppy seeds, if desired.
Bake buns at 350° for 15 to 18 minutes or until golden brown. Remove from pans, and cool on wire racks.