Place the potatoes in a saucepan and cover with the 4 cups of water. Bring to a boil, then add 1 teaspoon of the salt and cook, halfway covering the pan, until the potatoes are very tender.

Drain the potatoes, but save the water you boiled the potatoes in. Mash the potatoes well. (If you have a food mill or potato ricer, this would be a good time to use it. You want the potatoes to be very smooth.)

Measure the reserved potato water. You’ll need 3 cups of water, so if you are short, add more water to equal 3 cups.

Once the potato mixture has cooled to lukewarm, stir in the yeast. Let the mixture sit for 5 minutes.

Stir 2 cups of flour in plus the remaining 1 tablespoon of salt, then let the mixture sit another 5 minutes.

Add the softened butter and 1 more cup of flour. Mix to combine, then mix in another 2 cups of the all-purpose flour. Mix until fully incorporated.

If using a mixer, switch to the dough hook and continue to add flour, letting the dough mix well, until the dough is very soft. You will need to add between 1 1/2 to 2 1/2 cups more flour. Knead the dough for 6-8 minutes.

If making by hand, pour the dough out onto a generously floured surface. Knead the dough, adding flour as you do, until the dough is very soft. The dough will start out very sticky, so you  may need a dough scraper to keep the surface clean. Once the dough is not too sticky to knead, knead the dough for about 10 minutes.

Once the dough is mixed, place it in a large bowl that has been oiled. Turn to coat, then cover and let the dough rise until doubled in volume, about 2 hours.

Once risen, turn the dough out onto a floured surface and knead for a few minutes. Divide the dough into 2 equal portions.

Spray 2 9x5-inch loaf pans with nonstick cooking spray and set aside.

Working with one portion of dough at a time, roll the dough out into a large rectangle or oval, about 12x8-inches. Roll the dough to form a loaf. Pinch the seams together and tuck the ends under. Place in one of the prepared loaf pans. Repeat with the second half of the dough.

Cover with plastic wrap that has been sprayed with nonstick cooking spray and let it rise until puffy, about 45 minutes.

Preheat the oven to 350ºF. Place the loaves in the oven and bake until golden brown with an internal temperature between 190º and 200ºF, about 45 minutes.