1. Bring potato and water to cover to a boil in a saucepan over medium heat; boil 10 to 12 minutes or until tender. Drain, reserving 1 cup liquid, and cool potato 15 minutes. Press potato through a potato ricer or food mill, and cool completely (about 30 minutes).
2. Stir together yeast, 1 cup warm water, 2 tsp. sugar, and reserved cooking liquid in bowl of a heavy-duty electric stand mixer; let stand 5 minutes. Stir in eggs, next 3 ingredients, potato, 3 cups flour, and remaining sugar. Beat at medium speed, using paddle attachment, until smooth. Gradually beat in remaining 3 to 3 1/2 cups flour until a soft dough forms.
3. Turn dough out onto a well-floured surface, and knead until smooth and elastic (about 4 to 6 minutes), sprinkling with flour as needed. Place dough in a lightly greased large bowl, turning to grease top. Cover and let rise in a warm place (80° to 85°), about 1 hour or until doubled in bulk.
4. Punch dough down; turn out onto a lightly floured surface, and divide in half.
5. Gently shape each half into 12 (2 1/2-inch) balls, and place in 2 greased 10-inch round cake pans. Brush tops with 2 Tbsp. melted butter. Cover and let rise in a warm place (80° to 85°), 1 hour or until doubled in bulk.
6. Preheat oven to 375°. Bake 25 to 30 minutes or until rolls are deep golden brown. Remove from pans to a wire rack, and brush with remaining melted butter. Cool completely.
Prepare recipe through Step 4. Roll each dough half into an 18- x 9-inch rectangle. Starting at 1 short end, roll up each rectangle, jelly-roll fashion, pressing to seal edges as you roll. Pinch ends of dough, and tuck ends under. Place each roll, seam side down, in a lightly greased 9- x 5-inch loaf pan. Proceed with recipe as directed, baking 30 to 35 minutes or until deep golden brown.