Fill the rolls: After 10 minutes, roll the dough out in a 14×8-inch (36×20-cm) rectangle. Spread the softened butter on top. Mix together the cinnamon and brown sugar. Sprinkle it all over the dough. Roll up the dough to make a 14-inch log. Cut into 10–12 even rolls and arrange in a lightly greased 9- or 10-inch round cake pan, pie dish, or square baking pan.
Rise: Cover the pan with aluminum foil, plastic wrap, or a clean kitchen towel. Allow the rolls to rise in a relatively warm environment for 60–90 minutes or until double in size. (For a tiny reduction in rise time, see my answer to Where Should Dough Rise? in my Baking with Yeast Guide.)
Bake the rolls: After the rolls have doubled in size, preheat the oven to 375°F (190°C). Bake for 24–27 minutes, or until lightly browned. If you notice the tops are getting too brown too quickly, loosely tent the pan with aluminum foil and continue baking. If you want to be precise about their doneness, their internal temperature taken with an instant read thermometer should be around 195–200°F (91–93°C) when done. Remove pan from the oven and place pan on a wire rack as you make the icing. (You can also make the icing as the rolls bake.)
Make the icing: In a medium bowl using a handheld or stand mixer fitted with a paddle or whisk attachment, beat the cream cheese on high speed until smooth and creamy. Add the butter and beat until smooth and combined, then beat in the confectioners’ sugar and vanilla until combined. Using a knife or icing spatula, spread the icing over the warm rolls and serve immediately.
Cover leftover frosted or unfrosted rolls tightly and store at room temperature for up to 2 days or in the refrigerator for up to 5 days.
Notes
Make Ahead Instructions: This dough can be made the night before through step 4. Cover with plastic wrap and let rest in the refrigerator overnight. The next morning, remove from the refrigerator and allow to rise in a warm environment, about 1 hour. Continue with step 6.
Freezing Instructions: Baked rolls can be frozen up to 2–3 months. Thaw overnight in the refrigerator and warm up before enjoying. You can also freeze the unbaked rolls and here’s how: bake the rolls in step 6 for only about 10 minutes at 375°F (190°C). Cool completely, then cover tightly and freeze. To serve, take the pan of rolls out of the freezer and put into the refrigerator a few hours before serving. Then, finish baking them for the remaining 15–18 minutes.
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