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To make the dough: In the bowl of a stand mixer, whisk together the water, sugar, potato purée, butter, buttermilk, and eggs.
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Attach the mixer’s dough hook. Set the mixer speed to low and stir in the lesser amount of flour (5 1/2 cups, 660g), the yeast, and salt.
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Increase the speed to medium-low and knead the dough until it completely pulls away from the sides of the bowl, incorporating more flour (if necessary) a tablespoon or two at a time every 30 to 60 seconds.
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Increase the speed to medium-high and knead until the dough forms a smooth, elastic ball, about 5 minutes.
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Cover the bowl and let the dough rest in a warm place (70°F to 80°F is ideal) until it’s almost doubled in size, 1 to 1 1/2 hours.
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To make the filling: In a medium bowl, combine the brown sugar, cinnamon, and cornstarch. Set aside.
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To assemble the rolls: Transfer the dough to a lightly floured work surface that’s at least 24" x 30".
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Knead the dough a couple of times, then use a rolling pin to roll it into an 18" x 24" rectangle.
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Spread the softened butter over the surface of the dough, leaving a 1" strip of bare dough along one of the long sides. If the butter’s not soft enough to spread easily, beat briefly to soften.
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Sprinkle the filling over the butter, leaving the bare edge uncovered. Roll the dough gently with your rolling pin to help the filling adhere.
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Starting with the filling-covered long edge, roll the dough into a tight log. Pinch the seam shut at the end, first brushing the bare edge with a bit of water if necessary to get it to seal.
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Cut the log in half crosswise, then cut each half in half to make four smaller logs about 6" each. Cut each smaller log into thirds to make a total of 12 rolls about 2" long each.
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Grease two 9" x 13" pans and place six rolls in each pan (two rows of three). Gently press the rolls to flatten them slightly; loosely cover the pans with plastic.
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Put the pans in a warm place (at least 70°F) and allow the rolls to rise until they’ve doubled in size and are touching one another, 1 to 1 1/2 hours.
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Toward the end of the rise, preheat the oven to 350°F with one rack in the bottom third and one in the top third.
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Uncover the rolls and bake them for 20 to 25 minutes, rotating the pans halfway through, until golden brown and a digital thermometer inserted into the center of a roll reads 190°F; check a roll in each pan just to be sure. While the rolls are baking, make the frosting.
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To make the frosting: Beat the butter with a hand or stand mixer until light and fluffy. Add the confectioners’ sugar, 2 tablespoons (28g) of the cream, vanilla, lemon juice, and salt.
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Beat until the mixture is light and fluffy, 2 to 3 minutes, adding the additional 1 tablespoon (14g) cream if necessary to make a nicely spreadable frosting. Set aside.
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Remove the rolls from the oven and immediately spread the rolls with half the frosting. Allow the rolls to cool for 10 to 15 minutes, then spread them with the remaining frosting. Serve the rolls warm.
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Storage information: Store leftover Sweet Potato Cinnamon Rolls, well-wrapped, at room temperature for several days; or wrap baked, unfrosted rolls and freeze to reheat and frost at a later date.
