Start by bringing a large pot of salted water to a boil. Add the diced russet potatoes and cook until they are fork-tender, about 15-20 minutes. Once cooked, drain the potatoes, reserving 1 cup of the cooking water for later use.
In a bowl, mash the potatoes until smooth. You want them to be creamy with no lumps. Allow the potatoes to cool slightly before moving on to the next step.
In a small bowl, combine the reserved cooking water (make sure it's warm, not hot) with the sugar and yeast. Let this mixture sit for about 5-10 minutes until it becomes frothy, indicating that the yeast is activated.
In a large mixing bowl, combine the mashed potatoes, melted butter, egg, and salt. Stir to combine. Gradually add the frothy yeast mixture and mix until well incorporated.
Slowly add the all-purpose flour, one cup at a time, mixing until a soft dough forms. If the dough is too sticky, add a little more flour as needed. Knead the dough for about 5-7 minutes until it becomes smooth and elastic.
Transfer the dough to a lightly greased bowl, cover it with plastic wrap or a clean kitchen towel, and let it rise in a warm place until it doubles in size, about 1-2 hours.
Once the dough has risen, punch it down to release the air. Divide the dough into equal portions, depending on the size of buns you prefer. Shape each portion into a round bun and place them on a baking sheet lined with parchment paper.
Cover the shaped buns with a kitchen towel and let them rise again for about 30-45 minutes, or until they puff up.
During the last 10 minutes of the second rise, preheat your oven to 375°F (190°C).
Brush the tops of the risen buns with the egg wash (beaten egg mixed with water) and sprinkle with sesame seeds if desired. Bake in the preheated oven for 20-25 minutes, or until golden brown.
Once baked, remove the buns from the oven and let them cool on a wire rack. Enjoy them warm or at room temperature!
