Place potatoes in a saucepan, and cover with water. Bring to a boil, and cook until tender, about 15 minutes. Drain, cool, and mash.
In a large bowl, dissolve yeast in warm water. Let stand until creamy, about 10 minutes.
When yeast is ready, mix in 1 cup mashed potatoes, sugar, shortening, eggs, salt, and 3 cups flour. Stir in the remaining flour, 1/2 cup at a time, until dough has become stiff but still pliable. Turn dough out onto a lightly floured surface, and knead until smooth and elastic, about 8 minutes. Lightly oil a large bowl, place the dough in the bowl, and turn to coat with oil. Cover with plastic wrap, and refrigerate for at least 8 hours, and up to 5 days.
Deflate the dough, and turn it out onto a lightly floured surface. Divide the dough into two equal pieces, and form into rounds. Roll out each round to a 12 inch circle. Brush generously with melted butter, and cut each circle into 16 wedges. Roll wedges up tightly, starting with the large end. Place on lightly greased baking sheets with the points underneath, and the ends bent to form a crescent shape. Cover, and let rise for 1 hour. Meanwhile, preheat oven to 400 degrees F (200 degrees C).
Bake in preheated oven for 15 to 20 minutes, or until golden brown.