Preheat your oven to 375°F (190°C). Line a jelly roll pan with parchment paper and lightly spray with nonstick cooking spray.
In a large bowl, combine pumpkin puree, eggs, granulated sugar, and vanilla; mix until smooth.
In another bowl, whisk together flour, baking powder, cinnamon, and salt. Gradually fold the dry mixture into the wet ingredients.
Pour the batter into the prepared pan and spread evenly. Bake for about 15 minutes or until a toothpick comes out clean.
Immediately invert the cake onto a clean kitchen towel sprinkled with powdered sugar and roll it up from one short end while still warm.
Allow to cool completely in its rolled-up form.
For the filling: Beat softened cream cheese with powdered sugar and vanilla until smooth.
Once cooled, gently unroll the cake to spread the cream cheese filling evenly. Roll it back up without the towel and wrap in plastic wrap; refrigerate for at least an hour before slicing.