Peel and cut potatoes into ½-inch thick slices. Transfer to a medium pot, and fill with water until potatoes are covered by about an inch. Bring water to a boil over medium-high until potatoes are fork tender, about 10 minutes.

Drain potatoes, reserving ½ cup of the water. Mash the potatoes with a potato masher until smooth, and measure out 1 cup of mashed potatoes. (Save any remaining mashed potatoes for another use.) Allow the mashed potatoes to cool slightly, 5 to 10 minutes.

In the bowl of a stand mixer, whisk together the warm mashed potatoes, milk, sugar, yeast, and potato water until combined. Add the flour, salt, and butter, and using the paddle attachment on low speed, mix until just combined.

Using the dough hook attachment on low speed, knead the dough until smooth, tacky, and passes the windowpane test, 5 to 8 minutes. (To test the dough, pinch off a 1-inch ball, then stretch it between your fingers into a square. If the dough doesn’t break but is thin enough to let light pass through, it’s ready. If it breaks when stretched, continue kneading for another minute and repeat the test.)

Transfer the dough to a lightly oiled large bowl, cover, and let rise in a warm place until doubled in size, about 45 minutes.

Preheat oven to 350°F. Grease two 9x5-inch loaf pans.

Punch down the risen dough. On a lightly floured surface, divide the dough into 2 equal pieces (about 706g each). Gently press the first portion of dough into a 9x6-inch rectangle. Starting on one long side, fold the dough in on itself in thirds, pinching the seam together to seal it together. Reshape into a 9-inch log, if needed. Place into the prepared loaf pan, seam side down, and repeat with the second portion of dough. Loosely cover both loaves and let rise again until well puffed, about 20 minutes.

Uncover and bake until the tops are golden brown, 35 to 40 minutes. Let cool for a few minutes in the pan, then remove and cool completely on a wire rack. Store covered at room temperature for 3 to 5 days.