Put the potato in a medium saucepan with cold water to cover. Bring to a boil over medium-high heat and cook until tender, about 18 minutes. Drain, reserving 3/4 cup potato cooking water. Let the water cool until lukewarm (90 to 100 degrees F).
Use a ricer or food mill to puree the warm potato into the bowl of a stand mixer. (You can also mash with a masher; just make sure to get the potatoes very smooth.) Add the butter, honey and salt to the warm potatoes and stir until the butter is melted and the mixture is smooth. Add 1 egg, the yeast and the lukewarm cooking water. Mix with the dough hook on low speed to combine.
Add 3 1/2 cups of the flour and mix on low to combine. Knead on medium-high speed, adding up to 1/4 cup more flour, if needed, to make a smooth, slightly sticky dough that forms a loose ball on the dough hook, 6 to 8 minutes. Turn the dough onto a floured countertop and knead a few times to make a smooth ball. Oil a large bowl, add the ball and turn to coat. Cover loosely and let rise until doubled in size, 40 minutes to 1 hour.
Line 2 baking sheets with parchment paper.
Punch the dough down. Dust a clean, flat work surface with flour. Turn out the dough and cut it into 8 equal pieces. Working with one piece at a time, pinch the dough under itself to form a ball. With the pinched side down, cup your hands under the dough and rotate on the counter to form a smooth ball. Use one hand to roll the ball into a 4-inch-long oval roll. Place on a lined baking sheet and repeat with the remaining balls of dough. Cover with lightly oiled plastic wrap and let rise until light and airy looking, 30 to 40 minutes.
Place an oven rack in the lower and upper third positions. Preheat the oven to 400 degrees F.
When the dough has completed the second rise, beat the remaining egg with a tablespoon of water in a small bowl and gently brush the rolls with the egg wash. Sprinkle with the poppy seeds. Bake, rotating from top to bottom and back to front halfway through, about 20 minutes. Cool slightly on the baking sheets, then transfer to racks to cool completely. Rolls can be made a day ahead. For longer storage, wrap and freeze.
Tools You May Need
Tools You May Need
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