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1
In a small saucepan, combine the milk, squash puree and sugar and cook over low heat, whisking, until the milk is lukewarm and the sugar is dissolved.
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2
Remove the pan from the heat.
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3
Whisk in the yeast and egg; let stand until foamy, 10 minutes.
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4
In the bowl of a stand mixer fitted with the paddle, beat the 4 1/4 cups of flour and the salt at low speed just to combine.
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5
With the machine on, slowly add the warm milk mixture and beat until incorporated, about 1 minute.
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6
Beat in 1 tablespoon of the butter until completely incorporated; scrape down the side of the bowl.
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7
Add the remaining 7 tablespoons of butter, 1 tablespoon at a time.
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8
Beat the dough until well combined, about 2 minutes.
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9
Fit the mixer with the dough hook.
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10
Knead the dough at medium speed until smooth, occasionally scraping down the side of the bowl and dusting with 1 to 2 tablespoons of flour if the dough sticks, about 5 minutes.
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11
Transfer the dough to a lightly oiled bowl, turn to coat with oil and cover with plastic wrap.
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12
Let stand in a warm place until doubled in bulk, about 2 hours.
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13
Line 2 baking sheets with parchment paper.
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14
Gently press down on the dough; it should be tacky.
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15
Divide the dough into 36 equal pieces and cover with plastic wrap.
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16
Gently squeeze 1 piece of dough through your thumb and index finger to form a ball; pinch the bottom.
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17
Place the ball pinched side down on the prepared sheet.
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18
Repeat with the remaining pieces of dough, spacing the balls 1 1/2 inches apart.
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19
Loosely cover the rolls with plastic wrap and let rest in a warm place until doubled in size, about 1 hour.
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20
Preheat the oven to 400.
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21
Brush the tops of the rolls with the melted butter.
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22
Bake for 15 to 18 minutes, until golden and cooked through, shifting the pans from top to bottom and front to back halfway through baking.
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23
Serve warm.
