Wash potato and cut into large chunks. Cover with and boil in saucepan until potato is very tender, about 20 minutes. Save 1/2 cup of the potato water before draining. Drain potatoes, remove skin, and mash. Measure out 1 cup of the mashed potato.
Allow the potato water to cool to a lukewarm temperature. Add 1 tablespoon of the sugar (saving the other tablespoon for later) and dissolve yeast in warm potato water. Allow to sit and foam, undisturbed, for at least 5 minutes.
In the bowl your stand mixer using your paddle attachment, mix together the mashed potatoes, butter, eggs, remaining sugar, and salt. Mix together on medium speed for about 2 minutes.
To warm milk, heat in microwave for 45 seconds to 1 minute, or gently heat on stove over low heat. Combine with yeast mixture and stir. Add the yeast and milk mixture to the potato mixture. Mix on low speed until blended.
With the mixer running on low speed, add the flour 1 cup at a time and mix until a very soft dough forms. Change the paddle attachment out with the dough hook and knead on medium low speed for about five minutes. You want the dough to form a soft ball and pull away from the bowl. If it doesn't, add very small amounts of flour until it does.
Transfer bowl to a very large oiled bowl. Cover tightly with plastic wrap and allow to rise in warm place until it doubles in size, at least a couple hours.
Once risen, punch down dough. Turn out on surface with lots of flour. To make buns, measure out pieces of dough that are about 3.5 - 4 ounces in size. Form ball by tucking ends underneath. Place buns on a large jelly roll pan (I love to use mine with the silpat to prevent sticking or you can use parchment paper) about 1-2 inches apart. If using a large jelly roll pan, place them in a 4-3-4 pattern. Cover loosely with plastic wrap and allow to rise for at least 30 minutes.
Remove plastic wrap and bake in 350 degree F preheated oven for 15-20 minutes, until golden brown.
Can be stored in airtight container in freezer once cooled.