1. Heat 3/4 cup butter and milk in a large saucepan over medium-high heat to just below the boiling point. Add 3/4 cup sugar and 2 teaspoons salt, and stir until sugar dissolves. Remove from heat, and set aside to cool.
2. Combine yeast, 1 teaspoon sugar, and 1/2 cup warm water; let stand 5 minutes or until mixture becomes frothy.
3. Beat eggs, potatoes, and remaining 1/2 teaspoon salt at medium speed with an electric mixer until smooth and well blended; beat in 1/2 cup cold water.
4. Stir together the cooled milk mixture, egg mixture, and yeast mixture in a large bowl. Gradually add 3 cups flour, and continue beating at medium speed with an electric mixer. (You may have to beat in the rest of the flour with a wooden spoon.) Stir in 3 1/2 to 4 more cups flour or enough to form a soft dough, scraping down sides of bowl several times. (Dough will be very sticky.) Place dough in lightly oiled bowl; cover and refrigerate for 8 hours.
5. Preheat oven to 400°.
6. Lightly grease a 15- x 10- x 1-inch jellyroll pan. Remove dough from refrigerator, and punch down. Divide dough in half, and roll out each portion to 3/8- to 1/2-inch thickness; cut with a 2 1/2-inch biscuit cutter, and place on the prepared pan, with rolls just barely touching. Brush rolls with 3 tablespoons melted butter; fold each roll in half, pressing gently in the center to seal. Cover loosely, and let rise in a warm place (85°), free from drafts, 30 to 40 minutes or until doubled in size. Bake at 400° for 12 to 14 minutes or until golden brown.