Add the yeast to the buttermilk mixture and allow to sit until starting to foam; about 5 minutes.
In the bowl of a stand mixer fitted with the paddle attachment, add the yeast and buttermilk mixture, the potatoes, butter, beaten eggs, sugar and salt. Mix until just starting to combine; about 1 minute on medium.
Add 6 1/4 cups flour, change to the dough hook and mix until moistened and no dry pockets of flour remain. About 2 minutes on medium. Cover the bowl and let the dough rest 30 minutes.
Knead on a lightly floured counter 15 minutes, or in the machine on medium low 10 minutes until smooth and elastic.
Transfer to an oiled bowl turning to coat, or leave the dough in the mixer and lightly oil the top of the dough. Cover and rise 1 -1 1/2 hours
Grease two 9x5 loaf pans. Line with parchment paper for easier removal. Divide the dough in half, pressing out into a rectangle approximately 9 inches wide and 12 inches tall. Roll up the dough like sausage from the 9 inch side, and pinch the seam closed. Place the dough in the pan seam side down and let the dough rise until doubled--about 1 hour but just watch the dough.
When the dough is about 20 minutes away from being risen, preheat the oven to 375.
Beat one egg and brush over the dough. Bake 40-45 minutes until the internal temperature is 205. Tent with foil halfway through baking or when the bread reaches your preferred level of color.