Begin by peeling and chopping your russet potato into even cubes. Place the potato in a large pot of salted water, bringing it to a boil. Cook until tender, about 15-20 minutes. Once cooked, drain and mash the potato until smooth, then set aside ¾ cup of the cooking water for later use.

In a small bowl, combine the reserved lukewarm potato water, active dry yeast, and sugar. Gently stir and let it rest for 5-10 minutes until the mixture becomes bubbly and frothy.

In a large mixing bowl, combine the mashed potato, beaten egg, melted butter, honey, and salt. Stir the mixture until it’s well combined and smooth.

Gradually add the all-purpose flour and the activated yeast mixture to the potato mixture. Stir continuously until a soft dough forms.

Turn the dough out onto a floured surface. Knead it for about 5 minutes, folding and stretching until it becomes smooth and elastic. Once kneaded, shape it into a ball and place it in a greased bowl.

Cover the bowl with a clean kitchen towel and let it rise in a warm area for about 1 hour, or until it has doubled in size.

Once the dough has risen, punch it down gently to release air. Divide the dough into 12 equal pieces. Shape each piece into a smooth ball and place the shaped rolls on a parchment-lined baking sheet.

Cover the baking sheet with a towel and let the shaped rolls rise for another 30 minutes. Preheat your oven to 350°F (175°C).

Once the rolls have risen adequately, place them in the preheated oven. Bake for 15-20 minutes, or until the tops are lightly golden.

After baking, remove the rolls from the oven and allow them to cool slightly. Brush the warm rolls with melted flavored butter before serving.