Preheat oven to 350 F. Line a jelly roll pan ( 10 x 15″) with parchment paper & spray with baking spray.
With a hand mixer, beat eggs on high for 5 minutes, until frothy & dark yellow. Beat in sugar, oil & vanilla. In a small bowl, whisk together flour, baking powder, salt & spices. Stir into wet ingredients just until blended. Fold in dry carrots.
Spread batter in prepared pan. This makes a very thin layer; use a spatula to make sure it is spread evenly to the corners of pan. Bake 10-15 minutes. Test cake with a toothpick to be sure it is completely baked. While cake is baking, spread a clean kitchen towel on work surface. Sprinkle with powdered sugar. As soon as cake comes out of oven, turn it over on towel. Remove parchment paper carefully.
Working at the short end, fold the edge of the towel over cake. Using the help of the towel, roll cake tightly. Let cool completely while rolled, at least an hour.
Filling
While cake is cooling, make filling. Beat butter & cream cheese together until smooth. Stir in powdered sugar & vanilla; beat until smooth.
When cake is cool, carefully unroll the towel. Spread the filling evenly over cake & re-roll tightly. Chill about 30 minutes to an hour. Dust with powdered sugar, if desired, slice & serve.