Preheat the oven to 350°F (175°C) and prepare a baking pan.
In a mixing bowl, combine flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
In a separate bowl, beat the eggs and sugar until light and fluffy.
Stir in the pumpkin puree and vanilla extract until well combined.
Gradually add the dry ingredients to the wet mixture, folding gently to combine.
Pour the batter into the prepared baking pan and spread evenly.
Bake for 15-20 minutes until a toothpick inserted in the center comes out clean.
Let the cake cool in the pan for 5 minutes, then transfer it to a wire rack to cool completely.
While the cake is cooling, prepare the filling by beating cream cheese, powdered sugar, maple syrup, and spices until smooth.
Once the cake is completely cool, spread the cream cheese filling evenly over the top.
Carefully roll the cake from one end to the other, using the parchment paper to help.
Wrap the rolled cake in plastic wrap and refrigerate for at least one hour before slicing.
Slice and serve, optionally garnishing with whipped cream or a sprinkle of cinnamon.