1. Peel the potato and cut it into small pieces. Boil it in about 2 cups of water until tender. Strain the potato from the water, but keep the water. Set both aside to cool.

2. When the potato water reaches about 115F, add the yeast and let it sit for about 10 minutes to proof. While that’s sitting, mash the potato.

3. Mix together the yeast mixture, potato, sugar, salt, egg and butter until it is smooth. Add 2 cups of flour and continue to mix on low until it is incorporated. If you have a dough hook for your mixer, switch to it now. Scrape down the sides of the bowl. Then, with the machine on medium, add 2 cups of the flour, and let it incorporate. The batter should start to become a ball of dough. Continue to knead it for about 10 minutes. The dough will be moist, but basically soft and elastic. Add a bit more flour, if necessary, until it is no longer sticky to the touch but is still fairly moist.

4. Place the dough in a large plastic resealable bag, and let it sit in the refrigerator overnight (or place in a bowl lightly coated with oil, cover with plastic and let sit for about 4 hours in a warm room).

5. Lightly grease muffin tins.

6. After rising, knead the dough slightly on a well floured surface, then roll out to a 16x9-inch rectangle, until it is just less than 1/2 inch thick. You may need to adjust this size based on your muffin tins. You want the end rolls to fit into them easily, as they will rise more when cooking. If your muffin tins are on the small size, roll the dough to be longer and narrower for a smaller roll diameter. Dot the surface of the dough with the softened butter. Then, sprinkle the entire surface evenly with the cinnamon and brown sugar. Place a row of peaches along the bottom edge.

7. Now, carefully roll the dough over the peaches (this is a bit tricky). Tuck another row of peaches into the edge of the fold you just created, and roll again. Continue doing this until you are either out of peaches or the dough is completely rolled up.

8. Pinch the log closed, and gently roll it to seal. Using a sharp knife, slice the log into pieces about 1 inch thick, and carefully and quickly place the slice into a cup of the muffin tin. When all of the slices are done, cover with plastic wrap and set aside. The dough should continue to rise. Let them sit for about 30 minutes.

9. Preheat the oven to 350F. Bake the rolls for about 25 minutes, or until light golden brown. Let them cool on a wire rack in the tin for about 5 minutes, and then remove them from the tin.