Boil potato until tender. Drain cooking water, reserving 1/4 cup for use in the rolls. Finely mash the potato and measure out 1/2 cup. Let cool to room temperature.

In the bowl of a stand mixer, mix together mashed potato, butter, sugar, honey salt and egg with paddle attachment. Mix together on medium speed for about 2 minutes.

Combine yeast, warm milk and potato water and pour into mixer bowl. Mix on low speed until incorporated.

Gradually add flours, about a 1/2 cup at a time, until a soft dough forms. Switch to the dough hook attachment and knead on low speed for 5 minutes, adding more flour if necessary to achieve a soft dough that is slightly tacky but not sticky.

Transfer the dough to a lightly oiled bowl, turning once to coat. Cover with plastic wrap and let rise in a warm place until doubled in bulk, about 60-90 minutes.

Line a baking sheet with parchment paper. Turn the dough out onto a lightly floured surface and punch it down. Separate into 16 equal pieces and shape into rolls.

Place rolls on prepared baking sheet, about 1 1/2 inches apart. Sprinkle the rolls with a dusting of flour. Cover with a clean kitchen towel and let the dough rise again until the rolls have grown into each other, about 30-45 minutes.

Preheat oven to 400 degrees F.

Bake rolls for 12 minutes, or until golden brown. Serve warm.