Mix the flour, baking powder, baking soda, pumpkin pie spice and salt in a bowl. In another bowl, cream the eggs, sugar, vanilla and pumpkin puree. Combine wet and dry and mix slowly just until combined.

Line a cookie sheet with parchment paper and spray lightly with cooking spray. Tuck a few strips of parchment under the lining with the ends sticking out the sides so you can lift the cake out easily.

Spread the batter evenly over the sheet with a rubber spatula, pushing it into the corners and leveling it. Bake at 375°F for about 15 minutes, until the cake springs back when touched.

After a few minutes of cooling, lift the cake by the parchment strips and gently roll it up as tightly as possible. Cool on a wire rack with the seam on the bottom. Cooling it rolled keeps it from cracking later.

With a stand or hand mixer, cream the cream cheese, butter, vanilla and powdered sugar until smooth. Add a teaspoon of water if too thick, or more powdered sugar if too thin; it should hold its shape but spread easily.

Once the roll has cooled completely, unroll it and spread the frosting over the whole rectangle, leaving about 1 inch bare around the edges so it will not squeeze out.

Roll it back up and chill in the fridge until ready to serve.