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1
Combine egg yolks, whole egg, sugar, butter, and milk in the bowl of a stand mixer and whisk at medium speed. As the mixture comes together, add 10 ounces of the flour, along with the yeast and salt and continue whisking until combined.
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2
Remove the whisk attachment and replace it with a dough hook. Add remaining 5 ounces of the remaining flour and knead on low speed for 5 minutes. At this point, the dough should feel soft and moist but not sticky. If it is sticky, add a bit more flour (1 ounce at a time). Knead on low for another 5 minutes or until the dough clears the sides of the bowl. (I ended up using a total of 17 ounces.)
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3
Butter a 9 by 13-inch glass baking dish with the cold butter.
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4
Turn the dough out onto a lightly floured work surface and briefly knead. Gently shape into a rectangle with the long side nearest you. Then use a rolling pin to shape into 18 by 12-inch rectangle.
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5
For the filling, brush dough with the melted butter, leaving a 1-inch border along the top edge. Mix brown sugar, cinnamon and salt in a bowl. Sprinkle the brown sugar mixture over the dough, also avoiding the top border. Gently press the filling into the dough.
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6
Beginning with the long edge nearest you, roll the dough away from you into a tight cylinder. Firmly pinch the seam to seal and roll the cylinder seam side down. Very gently squeeze the cylinder to create even thickness.
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7
Using a serrated knife, gently cut the cylinder into 2-inch rolls; yielding 8 pieces. Arrange rolls cut side down in the baking dish; cover tightly with plastic wrap and store in the refrigerator overnight, or up to 16 hours.
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8
Heat oven to 200u00b0F. When the oven has reached 200u00b0F, turn it off and place the rolls in the turned-off oven. Let the rolls rise until they look slightly puffy, about 30 minutes.
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9
Without taking the rolls out of the oven, increase oven temperature to 350u00b0F and let rolls continue to bake for 25 to 30 minutes, until golden brown. Remove the rolls and let cool while you make the icing.
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10
For the icing, whisk cream cheese in the bowl of a stand mixer until creamy. Add milk and whisk until combined. Sift in powdered sugar and whisk until smooth. Spread over the rolls and serve immediately.
