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Let the bread dough come to room temperature on the counter. On a lightly floured surface roll the dough into a 13-inch by 11-inch rectangle. Position the rectangle so the 13-inch side is facing you. Brush the melted butter all over the dough, leaving a 1-inch border uncovered along the edge farthest away from you.
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Combine the brown sugar and cinnamon in a small bowl. Sprinkle the mixture evenly over the buttered dough, keeping the 1-inch border uncovered. Roll the dough into a log starting with the edge closest to you. Roll the dough tightly, making sure to roll evenly and push out any air pockets. When you get to the uncovered edge of the dough, press the dough onto the roll to seal it together.
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Cut the log into 8 pieces, slicing slowly with a sawing motion so you don’t flatten the dough. Turn the slices on their sides and cover with a clean kitchen towel. Let the rolls sit in the warmest part of your kitchen for 1½ to 2 hours to rise.
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To make the glaze, place the cream cheese and butter in a microwave-safe bowl. Soften the mixture in the microwave for 30 seconds at a time until it is easy to stir. Gradually add the powdered sugar and stir to combine. Add the vanilla extract and whisk until smooth. Set aside.
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When the rolls have risen, pre-heat the air fryer to 350ºF.
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Transfer 4 of the rolls to the air fryer basket. Air-fry for 5 minutes. Turn the rolls over and air-fry for another 4 minutes. Repeat with the remaining 4 rolls.
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Let the rolls cool for a couple of minutes before glazing. Spread large dollops of cream cheese glaze on top of the warm cinnamon rolls, allowing some of the glaze to drip down the side of the rolls. Serve warm and enjoy!