Beat eggs and sugar until thick, pale, and ribbons form (about 3–5 minutes).
Mix in pumpkin puree and vanilla extract.
Gently fold dry mixture into wet until just combined; don’t overmix.
Spread batter evenly into prepared pan. Bake for 13–15 minutes until springy to the touch.
Immediately invert cake onto a clean towel dusted with powdered sugar; peel off parchment; roll the cake and towel from short side. Let cool completely.
Beat cream cheese and butter until smooth. Add powdered sugar, vanilla (and salt if using), beat until fluffy.