Prepare the Cake Batter: Add discard, sugar, pumpkin puree, and egg yolks to your large bowl and mix until fully incorporated. In your medium bowl, combine flour, pumpkin spice, baking soda, and baking powder. Gradually add dry ingredients to wet, and whisk until there are no lumps.
Bake the Cake: Preheat oven to 350. Line your baking sheet with parchment paper and pour cake batter over parchment paper in an even layer. Bake for 15-20 minutes until center of the cake springs back when lightly pressed with a finger.
Roll the Cake: Coat tightly woven dish towel with powdered sugar and turn out baked cake onto the dish towel. Remove parchment paper from the bottom of the cake, then roll cake tightly on the shorter side.
Make Frosting: Place cream cheese, butter, powdered sugar, and vanilla extract in a bowl and mix until there are no lumps.
Frost the Pumpkin Roll: When the cake is fully cooled, gently unroll and smooth frosting onto the cake in an even layer. Roll cake back up and wrap in plastic wrap until ready to serve.