Peel the potatoes, cut into 1/2-inch slices, then add to 2 cups water in a saucepan. Boil until tender. Pour off the cooking water into a 2-cup measuring cup, adding additional water if necessary to make 1 3/4 cups. Add honey and butter to hot water to begin to soften. Mash the potatoes in the saucepan, then measure out enough to make 1 cup (any extra is a snack). Return mashed potato to pan, add the water mixture and stir until smooth. Set aside to cool to lukewarm.
In a large bowl or the bowl of a stand mixer, whisk together 4 1/2 cups of flour, yeast and salt. Make a well in the center and add the potato mixture. If mixing by hand, stir to combine until the mixture looks shaggy, then use your hands to bring the dough into a ball. With a stand mixer, use the dough hook attachment. Turn dough out into lightly floured surface, then knead for several minutes until dough is smooth and springy.
Place dough in prepared bowl, flipping so that the top surface is oiled. Cover tightly with plastic wrap and let rise in a warm place until almost doubled, about an hour.
Coat 2 (8-inch by 4-inch) loaf pans with oil or cooking spray.