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1
Mix 3 1/2 cups water, potato and 1 teaspoon salt in saucepan.
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2
Cover; boil until potato is very tender, about 20 minutes.
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3
Mash potato with cooking water until smooth.
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4
Transfer 2 cups potato-water mixture to bowl (discard any remaining mixture); cool to 105F to 115F.
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5
Whisk yeast, then pesto, sugar, pepper and remaining 1 teaspoon salt into potato mixture.
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6
Whisk in 1/2 cup melted butter, then eggs.
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7
Add enough flour, about 1/2 cup at a time, to form smooth and sticky dough, stirring vigorously with wood spoon.
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8
Butter large bowl.
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9
Transfer dough to bowl; turn to coat.
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10
Cover bowl with plastic wrap.
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11
For do-ahead version: Refrigerate dough overnight.
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12
For same-day version: Let dough rise in warm draft-free area until doubled in volume, about 45 minutes (do not punch down dough).
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13
Butter two 9-inch-diameter cake pans with 1 1/2-inch-high sides.
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14
Roll out dough on floured surface to 1/3-inch-thick round.
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15
Using floured 2 1/2-inch round cutter, cut out rounds.
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16
Reroll dough scraps and cut out additional rounds.
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17
Dip top of each dough round briefly into 6 tablespoons melted butter.
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18
Fold each dough round into half-circle, buttered surfaces pressed gently together.
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19
Arrange half of folded dough rounds side by side, with flared sides turned up, in each prepared pan.
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20
Cover loosely with plastic wrap and let rise in warm draft-free area until dough rounds are almost doubled in volume, about 30 minutes for chilled dough and 20 minutes for room-temperature dough.
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21
Meanwhile, position rack in center of oven; preheat to 400F.
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22
Bake rolls until golden, about 25 minutes.
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23
Cool in pans at least 20 minutes.
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24
Turn out.
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25
Serve warm or at room temperature.
