Peel the potato and cut into 1-inch cubes. Place into a small pot and cover with cold water by a couple of inches.

Bring to a boil, then reduce heat and simmer until tender, about 10 minutes.

Drain very well and mash until perfectly smooth. Let cool to no more than 110°F before proceeding.

Into the bowl of a stand mixer fitted with the dough hook (or a large mixing bowl, if you plan to knead by hand), place the bread flour, powdered milk, sugar, salt, and yeast. Whisk to combine well.

Add the water, honey, butter, mashed potato, and beaten egg.

Mix on low speed (number 2 on a KitchenAid mixer) until combined, and then let the machine run to knead the dough until it is fairly smooth and elastic, two to four minutes more. Dough will still be soft and sticky but should hold together.

Pour the safflower oil into a clean bowl and swirl to coat the bottom. Scrape dough out of mixer into bowl and turn to coat with oil.

Cover with plastic wrap and let rise until doubled in size, an hour or two depending on the the temperature of your kitchen.

Turn the dough out onto a lightly floured surface and use a bench knife to divide into 10 equal pieces. I like to weigh them for evenness — they'll be about (82 grams) each, depending on the size of your potato.

To shape each piece, fold it over onto itself a few times to create some surface tension, then roll into a 6-inch log with gently tapered ends. You can see this process in action in the video that accompanies this post.

Arrange buns in a hot dog pan, or on a silpat- or parchment-lined half sheet pan ¼ inch apart.

Cover again and let rise until doubled in size once more, about an hour. Buns will be connected along their sides.

Preheat oven to 350°F with a rack in the center.

When dough has doubled in size, use a very sharp knife or a lame if you have one to create a straight cut down the center of each bun's top, from end to end, to a depth of about ⅛ inch.

To make the egg wash, use a fork to whisk together the egg and milk in a small bowl.

Brush the buns with egg wash.

Bake for about 24 minutes, until golden brown on top and cooked through.

Remove from oven and let cool in pan on a cooling rack for 20 minutes.

Turn out of pan onto cooling rack, and let cool completely before proceeding.

To serve, use a serrated knife as necessary to separate buns. Using the split down the center of each bun as a starting point, use the knife to cut ⅔ of the way down each bun, leaving the bottom ⅓ attached.

Heat a cast iron skillet over medium-high, lightly spread the sides of each bun with softened butter, and toast on the skillet for a few minutes per side, until crisped and golden brown.