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1
Stir together warm water, yeast, and a pinch of the sugar in a small bowl and let stand until foamy, 5 to 10 minutes.
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2
(If mixture doesn't foam, discard and start over.)
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3
Put 5 cups flour, salt, and remaining sugar in bowl of electric mixer and mix with dough hook at low speed until combined.
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4
Whisk together milk and eggs in a small bowl, then add to dry ingredients along with yeast, beating at low speed until flour is incorporated.
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5
Beat at medium speed until a very soft dough forms, about 2 minutes.
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6
Add butter and continue beating at medium speed until dough is smooth, soft, and elastic, about 4 minutes (it will be quite sticky).
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7
Rinse a large bowl with hot water.
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8
Add dough to wet bowl and cover bowl tightly with plastic wrap.
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9
Let dough rise in a warm place until doubled in bulk, 45 minutes to 1 hour.
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10
Bring water and 1 cup granulated sugar to a boil, stirring until sugar is dissolved.
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11
Add cranberries and simmer just until they begin to burst, about 2 minutes.
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12
Pour through a large sieve into a bowl and cool berries, reserving syrup for another use (such as a flavoring for seltzer).
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13
Turn out dough onto a well-floured surface and dust with flour, then roll out into a 16-inch square.
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14
Brush off excess flour, then spread evenly with butter with a small metal offset spatula.
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15
Stir together brown sugar, cinnamon, and remaining 1/3 cup granulated sugar and sprinkle evenly over dough.
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16
Dot dough evenly with drained cranberries, then sprinkle with nuts if using.
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17
Beginning with side nearest you, roll up dough, firmly but not tightly, into a log, then pinch seam to seal.
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18
Trim 1 inch off each end with a large knife and discard, then cut log crosswise into 12 slices.
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19
Arrange slices, cut sides up, in buttered cake pans (place 1 slice in center of each pan, then evenly space 5 more around it).
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20
Cover with plastic wrap and let rise in a warm place until doubled in bulk, about 1 hour.
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21
Preheat oven to 350F while buns are rising.
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22
Bake buns in lower third of oven until puffed and golden, 30 to 35 minutes, then cool in pan on a rack 10 minutes.
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23
Stir together confectioners sugar and milk with a fork until smooth.
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24
Drizzle over buns while still hot.
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25
Serve buns warm or at room temperature.
