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1
Place the potato in a medium saucepan and cover with 2 1/2 cups water.
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2
Bring to a boil and cook until the potato pieces are very tender, about 15 minutes.
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3
Drain the potatoes, reserving 1 1/4 cups liquid and the potato pieces in separate bowls.
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4
Cool the potato liquid until it is lukewarm (110 to 115 F.).
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5
Add the yeast and let sit for 10 minutes.
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6
Mash the potato pieces until smooth.
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7
Measure 1/2 cup mashed potato.
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8
Using an electric mixer fitted with the paddle attachment, mix together the yeast mixture, mashed potato, granulated sugar, 1 1/2 teaspoons of the salt, 6 tablespoons of the butter, and the egg.
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9
Mix on low for 15 seconds.
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10
Add 2 cups of the flour and mix on low speed until thoroughly blended, about 1 minute.
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11
Switch to the dough hook attachment.
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12
Add 2 1/2 cups flour and knead at medium speed, adding more flour as needed to make a soft, elastic dough, about 10 minutes.
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13
Scrape the dough into a large plastic bag with enough room for the dough to expand 1 1/2 times in size.
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14
Seal the bag and place it in the refrigerator to rise overnight.
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15
Turn out the dough onto a lightly floured surface and knead it a few times to soften.
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16
Portion the dough into 16 equal pieces and roll each portion into a smooth ball.
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17
Mix 8 tablespoons of the butter and the remaining 1/4 teaspoon salt in a large, shallow bowl.
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18
Mix the brown sugar and cinnamon in a separate large, shallow bowl.
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19
Dip each bun in the butter, coating the entire surface, and then roll it in the brown sugar.
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20
Make sure there is plenty of the sugar and cinnamon mixture on each bun.
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21
Using a pastry brush, grease a 9 x 13-inch baking dish with the remaining 1 tablespoon butter.
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22
Place the buns in the dish, cover them with a piece of oiled plastic wrap, and let them rise in a warm, draft-free space until they are 1 1/2 times their original size, 45 minutes to 1 hour.
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23
Preheat the oven to 350 F.
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24
Bake the buns for about 25 minutes, or until they are light golden on top and a toothpick comes out clean when inserted in the middle of the center bun.
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25
Remove the buns from the oven and immediately turn them out onto a serving platter.
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26
Let the buns cool for at least 5 minutes.
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27
To serve, cut apart the buns.
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28
Place each bun on a small plate and drizzle with the syrup from the bottom of the baking dish.
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29
You can prepare the buns in advance, freeze them, and reheat them.
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30
Let the buns cool, wrap them in plastic wrap, and freeze for up to 1 month.
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31
To reheat, unwrap the buns and bake them in a 350F.
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32
oven for about 30 minutes.