Start by preheating your oven to 350°F so it's ready the moment your batter is done. In a large bowl, stir together the pumpkin puree, sugar, eggs, and vanilla until the mixture is smooth and well combined. This forms the moist, flavorful base of your cake.
In a separate bowl, whisk together the flour, baking soda, salt, and pumpkin pie spice. Mixing these dry ingredients on their own first keeps the baking soda evenly distributed so you don't end up with any odd-tasting bites later on.
Slowly fold the dry mixture into the pumpkin mixture, stirring just until no streaks of flour remain. The batter will be quite thin and pourable, which is exactly what you want for a thin, rollable cake layer.
Lightly grease your half-sheet pan with non-stick spray, then line it with wax paper, letting a little hang over the edges. Pour in the batter and spread it evenly with a spatula, then bake for exactly 15 minutes, until the top springs back when lightly touched.
Let the cake cool in the pan for about 10 minutes, then lift it out using the overhanging wax paper and set it on a cooling rack for another 10 minutes. While it's still slightly warm, roll the cake up together with the wax paper, starting from one short end, and let it cool completely in that rolled shape.
While the cake cools, beat the softened cream cheese, powdered sugar, butter, and vanilla together until smooth and fluffy. Try to resist tasting too much of it it's dangerously good on its own, straight from the bowl.
Once the cake is completely cool, gently unroll it and spread the cream cheese filling in an even layer across the whole surface. Carefully roll the cake back up, this time slowly peeling away the wax paper as you go instead of rolling it in.
Wrap the finished roll in a fresh piece of wax paper and refrigerate it for at least 4-6 hours, though overnight is even better. Chilling firms up the filling and makes slicing so much cleaner when you're ready to serve.