Preheat your oven to 350°F (175°C). Line a 10×15 inch jelly roll pan with parchment paper.
Prepare the Cake Batter: In a medium bowl, whisk together the flour, baking powder, and salt. In a large bowl, beat the eggs and granulated sugar until thick and pale. Add the vanilla extract, vegetable oil, milk, and lemon zest, and mix until combined. Gradually fold in the dry ingredients until just combined.
Bake the Cake: Pour the batter into the prepared pan and spread evenly. Bake for 10-12 minutes, or until the cake is lightly golden and springs back when touched.
Roll the Cake: While the cake is baking, prepare a clean kitchen towel and sprinkle it with powdered sugar. When the cake is done, immediately invert it onto the towel and carefully peel off the parchment paper. Starting at the short end, roll the cake up with the towel inside. Let it cool completely.
Make the Lemon Cream Filling: In a medium bowl, beat the cream cheese until smooth. Gradually add the powdered sugar, heavy cream, lemon juice, and lemon zest, and beat until light and fluffy.
Assemble the Cake: Unroll the cooled cake and spread the lemon cream filling evenly over the surface. Carefully re-roll the cake without the towel and place it on a serving platter.
Chill and Serve: Refrigerate the cake for at least 1 hour before slicing and serving. Dust with powdered sugar if desired.
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