In an electric mixer, whisk eggs and sugar on high for 5 minutes, until pale, thick, and doubled in volume.
Add the pumpkin, water, vegetable oil, and vanilla. Sift in flour, Pumpkin Pie Spice, and baking powder, and fold very gently so that you do not lose any of the airy volume.
Pour batter carefully onto Bake & Roll, spreading batter to all edges. Bake 10–12 minutes until golden brown.
To shape cake roll: while still warm, spread cake with Coconut Lime Dip. Using the Bake & Roll as a guide, starting at the short end, gently loosen cake while rolling snuggly into shape. Sit the cake seam-side down.
Slice into portions with a bread knife or chill until ready to serve.