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1
Make the dough: in a small pot, combine the milk and butter. Heat over medium heat, stirring, until the butter is just melted. Add the cold water to help cool the mixture - it should be just warm to the touch (about 85-95u00b0F) before you begin to mix the dough.
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2
In the bowl of an electric mixer fitted with the dough hook attachment, mix the flour, sugar, yeast, salt, the warm milk mixture, and egg on low speed for 3 minutes. Raise speed to medium and mix for 3 minutes more. Transfer to a greased bowl and cover with plastic wrap. Let rise for 1-1 1/2 hours - the dough will look noticeably puffy, but it may not fully double in size.
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3
While the dough rises, make the filling. In a medium pot, combine the blueberries, 1/4 cup (50 grams sugar), and the vanilla bean and its seeds. Heat over medium heat until the berries become soft and begin to break down. Transfer the mixture to a food processor or blender (or use an immersion blender right in the pot) to puree the mixture - vanilla bean and all - until it's relatively smooth.
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4
Return the blueberry mixture to the pot. In a small bowl, stir together the remaining 1/4 cup (49 grams) sugar with the cornstarch. Add this mixture to the blueberries and whisk well to combine. Bring to a simmer over medium low heat, stirring constantly. When the mixture begins to bubble, remove it from the heat and spread into an even layer on a baking sheet or casserole dish (this will help it cool quickly).
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5
When the dough has risen and the filling has cooled to room temperature, you can assemble the rolls. On a lightly floured surface, roll out the dough into a rectangle about 15 x 22 inches. Spread the filling into an even layer all over the surface of the dough - all the way to the edges.
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6
Starting with one of the shorter sides, begin to roll up the dough into a tight-spiraled log. With a bench knife (or regular chef's knife), cut the dough into eight even pieces. Instead of cutting straight down, cut the dough at a 45 degree angle to leave the sides angled to expose some of the swirled filling. Use your finger to press each roll down firmly on the top of each bun in the center to create a slight indent the surface.
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7
Transfer the rolls to a greased 9x13 inch pan - they should be just barely touching. Let rise for 30-45 minutes, until they've expanded slightly (they'll definitely be touching now!) and look noticeably puffy. Towards the end of rise time, preheat the oven to 375u00b0F. Brush the surface of the dough with egg wash, and bake until golden brown, 25-30 minutes.
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8
Let the buns cool for 10-15 minutes. While they cool, make the icing. In a medium bowl, whisk the powdered sugar, cream, and vanilla to combine. The mixture should be quite thick, because you'll apply it while the buns are still warm, and it will soften and spread a bit.
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9
Drizzle the icing all over the warm buns, and serve immediately (they're also good once they've cooled to room temperature, but warm - they simply can't be beat)!
