Boil the potatoes in salted water. Reserve ½ cup of the potato water. Drain well, then mash them with a handheld potato masher.
Gently whisk the water, yeast, and 1 tablespoon of sugar. Cover the measuring cup or bowl with plastic wrap and let it sit for about 7-10 minutes to bloom the yeast.
In a stand mixer with the dough hook, combine the yeast mixture, mashed potatoes, butter, salt, flour, rosemary, and remaining sugar. Start on low speed to incorporate the flour, then increase to medium speed and knead for about 7-8 minutes. You have kneaded the dough long enough when it pulls away from the side, has a smooth surface, and is tacky but not sticky.
Remove the dough to a lightly oiled bowl. Cover and let rise for about 1 hour or until doubled in size.
Gently punch it down by pressing a fist into the center of the dough, then cover and let it rise again for about 45 minutes or until doubled in size.
Place the Dutch oven in the oven and preheat to 425°F
Turn the dough onto a large piece of parchment paper. Sprinkle lightly with rosemary. Very carefully add the bread to the Dutch oven. The Dutch oven and its lid will be extremely hot, so handle them with care.
Bake covered for 30 minutes. Reduce the oven temperature to 375°F, uncover, and bake for 10 minutes or until golden brown and the internal temperature reaches 190°F-200°F. Cool for 1-2 hours before slicing with a serrated knife.