Peel and dice the potato. Add the potato to a saucepan and cover with a couple inches of water. Bring to a boil and cook until tender. Drain the potatoes but save 1 ¼ cups of potato water. Allow the potato water to cool down to between 105°F to 115°F. Mash the boiled potatoes and set aside.
In a small bowl combine ½ cup of the warm potato water with the sugar and the active dry yeast. Stir briefly and then set aside for the yeast to activate. When the yeast is bubbly and risen, after about 5 minutes, proceed with the recipe.
In the bowl of a stand mixer add the remaining ¾ cup of warm potato water, the mashed potatoes, the beaten eggs, melted butter, honey, and the yeast mixture. Add 5 cups of the flour and the salt and attach the dough hook.
Mix, using the dough hook, until the dough starts to come together. Scrape down the sides occasionally to encourage the dough to come together. This is a soft and somewhat sticky dough so you will likely need to add extra flour, a tablespoon at a time, to prevent the dough from sticking to the bowl.
Continue mixing with a dough hook for about 5 minutes until the dough is soft and stretchy. Turn the dough out onto a floured counter and knead to bring it together into a smooth ball. Transfer the dough to a greased bowl. Drizzle a little more oil on top of the dough and rub it all over. Cover with cling film or a tea towel and then set in a warm place to rise for 1 hour.
After the dough has risen for 1 hour, punch it down to deflate completely. Lightly knead the dough to remove any air bubbles. Divide the dough in quarters.
Shape each quarter into a short, thin loaf, similar to a small baguette, about 9-10 inches long. Transfer the loaves to parchment lined baking sheets. Use kitchen shears to snip the loaves into individual rolls. Make 4 or 5 deep cuts, not all the way through, at about a 45° angle. Alternate the cuts between each side. Gently pull each roll to the side to create a wheat sheaf appearance. Repeat with each loaf. Alternatively, shape into individual rolls.
Lightly dust the rolls with flour to prevent them sticking. Cover with a tea towel and let rise for 30 minutes.
While the dough is rising, preheat the oven to 400°F. Bake the loaves for 20 to 25 minutes until golden brown and cooked all the way through. Rotate the pans in the oven after 15 minutes to encourage even browning. Let cool before serving.