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In the bowl of a stand mixer fitted with a paddle attachment (or in a large bowl if mixing my hand), stir together the milk, yeast, and sugar.
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Let the yeast mixture stand for 5-10 minutes, or until foamy.
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Add the remaining roll ingredients, and stir until dough comes together.
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Once the dough comes together, switch to the dough hook (if using the stand mixer), and knead for 5 minutes (or about 8-10 minutes by hand).
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Put dough into a lightly greased bowl, turning to coat.
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Cover, and let dough rise until doubled in size, about 1-1 1/2 hours.
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Toward the end of the rising time, prepare the filling.
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In a small bowl, stir together sugars and cinnamon.
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In a separate small bowl, stir together butter and vanilla extract.
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Once the dough has risen, roll dough into a 16x21-inch rectangle.
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Brush butter mixture over dough, and then sprinkle cinnamon-sugar mixture evenly over dough.
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Roll dough up tightly lengthwise, and cut into 12 rolls.
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Place rolls cut side up in a lightly greased 9x13 inch baking pan.
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Cover, and let rise until just about doubled, about 30 minutes.
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Toward the end of the second rising, preheat oven to 400 F.
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Uncover rolls and bake for about 15 minutes, or until lightly golden brown.
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While rolls are baking, prepare the frosting.
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In a medium bowl, beat together cream cheese, butter, powdered sugar, milk, vanilla extract, and salt.
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Let rolls cool for about 5-10 minutes, or until warm but not hot.
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Spread frosting on warm rolls before serving.