Preheat the oven to 350°F.
Grease the bottom and sides of a 10 x 15-inch sheet pan (Note 2). Line the bottom and sides of the pan with parchment paper, then grease the parchment paper.
Whisk the flour, sugar, brown sugar, baking powder, baking soda, pumpkin pie spice, cinnamon, and salt together in a large mixing bowl.
Stir the pumpkin puree, milk, vanilla extract, and apple cider vinegar together in a small bowl or container.
Add the pumpkin mixture to the bowl containing the flour mixture. Whisk or stir just until the batter is fully mixed.
Transfer the batter to the prepared sheet pan, smoothing out the top as evenly as possible (Note 3).
Bake the cake for 13 to 15 minutes, until the top feels set.
While the cake bakes, arrange a woven kitchen towel or a large sheet of cheesecloth on the counter. Dust the top with a heavy coating of powdered sugar — use at least ½ cup.
When the cake comes out of the oven, immediately invert it onto the prepared cloth. Roll the cake up in the towel, starting from one of the shorter ends. Don't roll it too tightly, or it will be difficult to unroll later on. Carefully place the rolled cake onto a cooling rack and let it cool completely, at least 2 to 3 hours.
Once the cake is cool, make the filling. Beat the cream cheese and butter together using an electric mixer on high speed, until fully blended. Begin beating in the powdered sugar, adding it in 2 or 3 increments. Once all of the powdered sugar has been added, beat in the vanilla (Note 4).
Very carefully unroll the cake, doing your best to avoid cracking it. If it gets challenging, you can leave the very end slightly rolled, just opening it up enough to stuff some filling in there.
Spread the filling in an even layer over the cake, leaving about an inch border at the short ends, ½ inch at the long ends.
Carefully roll the cake back up.
Wrap the pumpkin roll in plastic wrap, then chill it in the fridge for at least two hours.
Unwrap the pumpkin roll and dust it with powdered sugar. Slice and serve.