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1
Make the dough the day before you want to bake the rolls. To make the dough, combine the flour, yeast, salt, and sugar in the bowl of an electric mixer fitted with the dough hook. Mix on low speed for 20 to 30 seconds, just to combine.
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2
Stir the butter or shortening into the warm mashed potatoes and stir to combine (and until the fat is melted).
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3
Add the water, the potato mixture, and the eggs and mix on low speed for 4 minutes. Scrape down the bowl and scrape the dough away from the hook. Raise the speed to medium and mix for 3 minutes more. The dough may be a little sticky: That's okay.
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4
Transfer the dough to a large, oiled bowl and cover with plastic wrap. Let the dough rise at room temperature for 1 hour. Transfer the dough to the refrigerator and let rise overnight. (Mama says to use a BIG container and check the dough periodically, punching it down as needed to prevent overflow).
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5
The day you want to bake the rolls, bring the dough to room temperature (about 30 to 45 minutes).
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6
Divide the dough into even pieces (18 if you want to make plain rolls, 36 if you want to make split-top rolls, or 54 small pieces if you want to make clover rolls). I weigh the dough and then do the math to figure out how much each piece should weigh, but eyeballing is okay too!
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7
On a lightly floured surface, roll each piece of dough into a tight ball. The best way to do this is to use the heel of your hand, making a circular motion upwards toward your thumb, then back down to the base of your hand (see photograph).
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8
Preheat the oven to 375u00b0 F. Grease muffin pans with some of the melted butter.
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9
Place the balls of dough (1 for plain, 2 for split-top, 3 for clover rolls) in each cavity of the baking tin. Cover the rolls with a damp, clean towel and let rise for 1 hour. (Mama says to brush them with a little butter here to keep the tops from drying out, but the towel is usually enough if you want to wait.)
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10
Brush the risen rolls with melted butter. Bake until deeply golden brown, 20 to 25 minutes (a thermometer inserted into the center should read 200 to 215u00b0 F).
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11
When the rolls come out, brush them with melted butter (yes, again-thus is the genius of my mother). Serve warm, ideally.
