Start by cooking one large peeled and cubed potato in 1 ½ cups of water with ½ teaspoon of salt until it's fork-tender. Once cooked, mash the potato with 3 tablespoons of the cooking water using a fork.
Measure out ½ cup of the mashed potato and set it aside. If you have leftover mashed potatoes, you can use that instead.
Combine the mashed potato with ¾ cup of buttermilk and mix well. Allow the mixture to cool until it is warm but not hot.
In the warm potato buttermilk mixture, whisk in 1 tablespoon of honey, 2 ½ teaspoons of active dry yeast, and 1 tablespoon of flour. Mix thoroughly and let it sit for 5-8 minutes until it becomes foamy.
In a separate bowl, add 3 cups of all-purpose flour, ¼ teaspoon of salt, and ⅛ teaspoon of ground black pepper. Stir to combine and set aside.
Make a well in the center of the flour mixture and add 2 large room temperature eggs, 5 tablespoons of softened butter, and the yeast mixture. Stir with a wooden spoon until everything is combined, about 30 seconds.
Using a stand mixer with a hook attachment, knead the dough for 8 minutes until it becomes soft. If the dough is too wet, you can add up to ¼ cup of flour, adding it a tablespoon at a time. The dough should be smooth but will not form a ball in the mixer.
Transfer the dough to a lightly floured surface and knead it for an additional 30 seconds to 1 minute until it forms a ball. Place the dough in a lightly oiled bowl, cover it, and let it rise in a warm place for 1 hour.
After the dough has risen, turn the bowl upside down onto a lightly floured parchment sheet or silicone mat. Weigh the dough and divide it into 8-9 equal pieces, or more if you prefer smaller buns. Each large bun should weigh about 125 grams.
Shape each piece of dough into a ball and place them on a baking sheet lined with parchment or a silicone mat. Cover the buns with a kitchen towel and let them rise for 45 minutes.
Preheat your oven to 375°F (195°C). In a small bowl, whisk together 1 egg and 1 tablespoon of water. Brush the risen buns with this egg wash, being careful not to let it pool around the buns.
If desired, sprinkle the buns with poppy seeds, sesame seeds, or coarse salt. Bake in the preheated oven until they are golden brown: large buns for 18-20 minutes and small buns for 15-16 minutes.
Once baked, remove the buns from the oven and cover them with a dry kitchen towel for 15 minutes. After that, remove the towel and let the buns cool completely.
