Preheat your oven to 350°F (175°C). Line a 10x15-inch jelly roll pan with foil, then give it a good spray with floured nonstick cooking spray to prevent sticking.
In a large bowl (or stand mixer), beat the eggs on medium speed for a full 5 minutes until they're light, foamy, and pale yellow. Next, add ¾ cup granulated sugar and continue mixing for 2 more minutes until the mixture thickens a bit. Stir in the oil, baking powder, salt, and vanilla. Finally, gently mix in the all-purpose flour until just combined – don't overmix!
Pour the batter evenly into your prepared pan, spreading it out with a spatula. Tap the pan lightly on the counter a couple of times to release any air bubbles. Bake for 10-15 minutes, or until the top looks golden and springs back gently when touched.
While your cake bakes, lay a clean kitchen towel flat on your counter and sprinkle it generously with about ¼ cup of powdered sugar. This prevents sticking.
As soon as the cake is out of the oven, carefully flip it hot onto the sugared towel (use oven mitts!). Gently peel off the hot pan and foil. Now, starting from the short side, roll the cake up tightly with the towel inside. Let this rolled cake cool completely while still rolled in the towel.
In a large bowl, beat the softened cream cheese and ½ cup granulated sugar until it's super smooth and fluffy. Blend in the vanilla. Slowly pour in the cold heavy whipping cream, then crank up the mixer to high speed and beat until you have firm, stiff peaks. This makes a wonderfully stable whipped cream!
Wash and thoroughly dry your strawberries. Slice about ¾ of the pound into small, bite-sized pieces, and pat them dry again to remove excess moisture. Gently unroll your cooled cake. Spread a generous layer of the cream cheese whipped cream over the cake, then sprinkle the chopped strawberries evenly on top. Carefully roll the cake back up as snugly as you can, gently peeling it from the towel as you go. Wrap the finished cake roll in plastic wrap and chill it in the fridge until you're ready to serve.
Before serving, frost the outside of the cake roll with the remaining whipped cream and decorate with any extra fresh strawberries. Slice and share this beautiful, fruity dessert!