Prep the pan and ingredients for assembly. Line a quarter sheet pan with parchment paper.Melt the butter in the microwave (or in a small, heavy-bottomed saucepan over medium-low heat). In a small bowl, whisk together the sugar and cinnamon. Shape the dough. Uncover the dough and discard the plastic wrap. Tip it onto a lightly floured counter. Use a rolling pin to roll the dough into a large rectangle about 12 inches wide and 20 inches long. Press a bench scraper against the sides of the dough to create straight edges. Fill the dough. Pour the melted butter into the center of the dough and use an offset spatula or pastry brush to spread it evenly to the edges. Sprinkle the cinnamon sugar mixture over the butter. Spoon the apple pie filling over the mixture, distributing it randomly but evenly. Roll and cut the dough. Starting from one of the short ends, roll the dough into a log. Use a serrated knife to cut the log crosswise into 6 rolls, each about 2 inches wide.
Proof the rolls. Place the rolls cut-side up and at least 3 inches apart on the prepared pan. Cover with plastic wrap and let sit in a warm spot for 1 to 2 hours, or until doubled in size.
Prep the oven. About 30 minutes into the second rise, position a rack in the center of the oven and preheat to 350°F.
Meanwhile, make the glaze. In a medium bowl, whisk together the confectioners’ sugar, sour cream, milk, and vanilla. Cover loosely with plastic wrap and refrigerate while you wait for the rolls to finish proofing and baking.
Bake the rolls. Bake the rolls for 30 to 35 minutes, or until the edges are golden brown and a skewer inserted into the center of a roll comes out clean.
Glaze the rolls. Immediately spoon about 1 Tablespoon of glaze on top of each roll, using an offset spatula as necessary to spread the glaze. Sprinkle with the pie streusel.
Serve and store. Serve warm, or at room temperature. The cinnamon rolls can be stored at room temperature, under a cake dome or a large bowl turned upside down, for up to 1 day. After that, transfer the cinnamon rolls to an airtight container and refrigerate for up to 2 days more.