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1. FOR THE FILLING: Combine brown sugar, granulated sugar, cinnamon, and salt in bowl. Stir in melted butter and vanilla until mixture resembles wet sand; set aside.
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2. FOR THE DOUGH: Grease dark 9-inch round cake pan, line with parchment paper, and grease parchment. Pour 1/4 cup milk in small bowl and microwave until 110 degrees, 15 to 20 seconds. Stir in yeast and 1 teaspoon sugar and let sit until mixture is bubbly, about 5 minutes.
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3. Whisk flour, baking powder, salt, and remaining 5 teaspoons sugar together in large bowl. Stir in 2 tablespoons butter, yeast mixture, and remaining 1 cup milk until dough forms (dough will be sticky). Transfer dough to well-floured counter and knead until smooth ball forms, about 2 minutes.
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4. Roll dough into 12 by 9-inch rectangle, with long side parallel to counter edge. Brush dough all over with 2 tablespoons butter, leaving 1/2-inch border on far edge. Sprinkle dough evenly with filling, then press filling firmly into dough. Using bench scraper or metal spatula, loosen dough from counter. Roll dough away from you into tight log and pinch seam to seal.
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5. Roll log seam side down and cut into 8 equal pieces. Stand buns on end and gently re-form ends that were pinched during cutting. Place 1 bun in center of prepared pan and others around perimeter of pan, seam sides facing inches Brush tops of buns with remaining 2 tablespoons butter. Cover buns loosely with plastic wrap and let rise for 30 minutes. Adjust oven rack to middle position and heat oven to 350 degrees.
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6. Discard plastic and bake buns until edges are well browned, 23 to 25 minutes. Loosen buns from sides of pan with paring knife and let cool for 5 minutes. Invert large plate over cake pan. Using potholders, flip plate and pan upside down; remove pan and parchment. Reinvert buns onto wire rack, set wire rack inside parchment-lined rimmed baking sheet, and let cool for 5 minutes.
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7. FOR THE GLAZE: Place cream cheese in large bowl and whisk in butter, milk, vanilla, and salt until smooth. Whisk in sugar until smooth. Pour glaze evenly over tops of buns, spreading with spatula to cover. Serve.
