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Dough: Grease a large mixing bowl with butter and set aside.
Place yeast with 1 teaspoon sugar and half of the warmed milk in the bowl of the mixer. Combine, cover bowl with plastic wrap and let mixture sit for 5 minutes.
In a small bowl combine remaining milk with the whole eggs, the yolk and vanilla. Add this to yeast mixture and combine. Add remaining sugar and flour and mix on low speed with dough hook until combined. Add salt and mix 45 seconds more. Increase mixer’s speed and continue beating for 2 – 3 minutes, while gradually adding soft butter. Beat for 2 more minutes, remove dough from bowl and transfer to greased bowl, rolling dough over in the bowl to coat it with butter. Cover bowl with plastic wrap and let sit at room temperature for
2 hours. Dough will have doubled in volume. Press down dough in the center to deflate and fold it over. Cover again with plastic wrap and refrigerate for 1 hour.
Grease a 9 x 13-inch (18 x 26 cm) baking dish with soft butter.
Remove dough from refrigerator, dust work surface with flour and place dough over it. Turn dough lightly on surface to coat it with flour. Sprinkle more flour if necessary. Roll dough using a rolling pin into a 16 x 20 inch (32 x 40 cm) rectangle. Spread ½ cup soft butter over dough, leaving a 1-inch (2 cm) border at top and bottom.
Filling: Combine brown sugar with cinnamon in a bowl and pour in the center of the dough.
Spread mixture, with hands, over the butter. Roll dough, carefully, from bottom to top into a tight cylinder. Once cylinder is formed cut 12 equal pieces and transfer them, with cut side down in greased baking sheet, one next to the other. Refrigerate overnight or for 6 hours. The following day, remove rolls from the refrigerator and leave them at room temperature for 30 minutes.
Bake in preheated oven to 375°F (190°C) for 24 to 26 minutes until rolls are golden brown.
Remove from oven and invert onto a cooling rack lined with aluminum foil. Cool for 15 minutes.
Topping: Combine cream cheese with sugar in a small bowl until creamy. Stir in milk. Once rolls have cooled, spoon 2 tablespoons glaze over each roll and spread with the back of the spoon to the edges. Set aside for 5 minutes, before serving.
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