In the bowl of a stand mixer, combine the yeast, sugar, lukewarm water, softened butter, salt, and eggs. Add the mashed potatoes and mix with the paddle attachment on low speed until combined.
Add the flour to the bowl. Mix on low speed until a shaggy dough forms and most of the flour is incorporated.
Switch to the dough hook. Knead on medium speed for 7 to 8 minutes. The dough should become smooth, shiny, and pull away from the sides of the bowl, though it will still be soft.
Transfer the dough to a large, lightly greased bowl. Cover the bowl with plastic wrap and refrigerate for at least 8 hours, or up to 24 hours.
Grease two 9x5-inch loaf pans. Remove the cold dough from the refrigerator, place it on a lightly floured surface, and divide it in half.
Shape each half into a log about 9 inches long and place them seam-side down in the prepared pans.
Cover the pans loosely with greased plastic wrap. Let the loaves rise in a warm, draft-free place for 2 to 4 hours, or until the dough has risen about 1 inch above the rim of the pans.
Near the end of the rising time, preheat your oven to 350°F (175°C).
Bake the loaves for 25 minutes. Tent the pans with aluminum foil to prevent over-browning and continue to bake for another 15 to 20 minutes.
The bread is done when it is deep golden brown and an instant-read thermometer inserted into the center registers 190°F (88°C). Let the loaves cool in the pans for 5 minutes before turning them out onto a wire rack to cool completely before slicing.