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To prepare the potato: Cut the potato (no need to peel) into 1/2" cubes and place in a small saucepan. Cover with cold water and bring to a boil over medium-high heat. Once boiling, reduce the heat to medium-low and simmer until the potato pieces are fork-tender, 7 to 10 minutes. Drain, reserving the potato cooking water.
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Transfer 1 cup (163g) of the potato pieces to the bowl of a stand mixer fitted with the dough hook. Turn the speed to medium and mash the potatoes just until roughly broken up, with some large and small pieces, about 30 seconds.
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To make the dough: Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. Add 3 tablespoons (43g) of the reserved warm potato cooking water to the mixer bowl, along with the flour, egg, sugar, butter, sour cream, yeast, and salt. Mix on low speed until a shaggy mass forms, about 30 seconds. Scrape the bowl and mix on medium speed to form a tacky dough that clears the sides of the bowl, 30 to 60 seconds more.
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Add the bacon, cheese, and chives and mix on medium speed for 2 to 3 minutes, stopping to scrape the bowl halfway through. The dough will be soft and sticky and will not clear the sides of the bowl, but resist the urge to add more flour.
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Scrape the dough into a ball, cover the bowl, and let rise at room temperature for 30 minutes. The dough may not rise much during this time.
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To perform a bowl fold: Use a wet hand to grab a section of dough from one side of the bowl, lift it up, then press it down into the middle. Repeat this motion 6 to 8 times, grabbing a new section of dough each time until you've made a full circle around the bowl. Once you’ve completed the bowl fold, turn the dough over in the bowl so that the smooth side is up. Re-cover the bowl and let the dough rise for another 30 minutes.
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Using a wet hand, repeat the bowl fold. At this point, the dough should be smoother and feel tighter. Cover the dough and let rise for another 30 minutes, until the dough is puffy but not necessarily doubled in size.
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Line an 8" square pan with a parchment sling and lightly grease the parchment.
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Gently deflate the dough and transfer it to a well-floured work surface. Flour the top, then divide the dough into 9 equal pieces (about 80g each).
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Shape each piece into a rough ball by pulling and gathering the dough into a very small knot. Place the pieces seam side down and roll each under a cupped hand to form a smooth ball. Use additional flour as needed to prevent sticking.
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Place the shaped rolls in the prepared pan. Cover and let rise until puffy and a small indentation remains when pressed with a floured fingertip, 45 to 60 minutes.
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While the dough is rising, preheat the oven to 350°F with a rack in the center.
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Bake the potato rolls for 25 to 30 minutes, or until well browned on top and pale around the edges and an instant-read thermometer inserted into the center registers at least 190°F.
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To add the toppings: Remove the pan from the oven and brush the rolls with melted butter. Sprinkle the cheese and bacon on top and return to the oven for another 3 to 5 minutes, until the cheese is melted. Remove from the oven and dab the rolls with any remaining butter before sprinkling with chives and flaky sea salt.
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Allow the potato rolls to cool in the pan for 5 minutes, then use the parchment sling to lift them out and place them onto a rack. Serve warm or at room temperature.
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Storage information: Store cooled rolls, tightly wrapped, at room temperature for several days; freeze for longer storage.
