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Preheat the oven to 400°F. Lightly grease a 9" round cake pan. If desired, melt 2 tablespoons butter, and drizzle it into the bottom of the prepared pan. This adds to the buns' buttery flavor.
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To make the dough: In a medium-sized mixing bowl, whisk together the flour, leavener(s), salt, and sugar.
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Cut the butter into pieces, and work it into the dry ingredients until the mixture is unevenly crumbly.
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Break an egg into a measuring cup, and add milk to the 1/2-cup line.
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Whisk them together, and add to the dry ingredients, stirring to make a soft dough.
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Transfer the dough to a heavily floured work surface, and roll it into a rope about 14" long.
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Flatten it gently, then use a rolling pin to gently roll it into a 16" x 6" rectangle. Use a dough scraper or giant spatula to lift the dough as you roll, adding more flour underneath if it begins to stick to the work surface.
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To make the filling: Combine all of the filling ingredients, mixing until smooth and spreadable.
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Spread the filling on the rolled-out dough, leaving a 1" margin free along one long edge.
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Starting with the long edge that DOES have filling on it, roll the log up. Turn it so the seam is on the bottom, and gently shape it until it's about 16" long.
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To form and bake the buns: Cut the log into 16 slices, and place them in the prepared pan.
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Cover the pan, and refrigerate overnight, if desired. Or you can bake the buns immediately.
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Whether they've been refrigerated or not, bake the buns for 20 to 25 minutes (the longer amount of time if they've been chilled), until they're just beginning to turn a light golden brown.
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Remove them from the oven, and place them on a rack to cool, as you prepare the frosting.
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To make the frosting: Stir together the sugar, vanilla, butter, and salt.
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Add 1 1/2 tablespoons milk or cream, and beat until smooth and creamy, adding additional liquid if the frosting seems too thick to spread easily.
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Spread the frosting on the warm buns. Serve warm, or at room temperature.
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Buns will stay soft for several days, so long as you keep them covered.