Preheat oven to 350°Line a 10 x15” cake/jelly roll pan with foil and spray with floured nonstick cooking spray.
Place eggs in a large bowl or the bowl of an electric mixer. Beat at medium speed with mixer for 5 minutes until foamy and yellow.
Add sugar and mix for 2 more minutes, until the mixture is thickened slightly. Mix in oil, baking powder, salt, and vanilla, then add flour and mix slowly until just combined.
Pour into prepared pan, spreading as needed with a spatula. Tap the pan twice on the counter to release air bubbles, then bake for 10-15 minutes, or until the top is browned and the cake springs back when touched lightly.
While the cake is baking, lay out a clean kitchen towel onto the counter. Spread with about 1/4 cup powdered sugar.
Remove the hot cake from the oven and carefully, using oven mitts so you don’t burn yourself, flip the cake onto the towel (This might make a mess). Carefully remove the pan and foil and then, using the towel, roll the cake up from the short side. Note: The towel will be rolled into the cake. Don’t worry, this is supposed to happen. Let cool completely before continuing.
Note: You can wrap the cooled cake in plastic wrap and let it sit overnight before finishing.
The filling: Place cream cheese and sugar in a large bowl or the bowl of an electric mixer. Use mixer to beat the cream cheese and sugar until it’s smooth and fluffy, then beat in vanilla. Slowly add the heavy whipping cream, then turn the mixer to high and beat until stiff peaks form.
To fill cake: wash and dry the berries thoroughly. Slice about 3/4 of a pound into small pieces, then pat the pieces dry. Carefully unroll the cake. Spread with some of the whipped cream mixture and top with the chopped strawberries. Carefully roll the cake back up as tight as possible, releasing it from the towel as you go. Wrap the cake roll in plastic wrap and chill until ready to top and serve.
To serve: frost with remaining whipped cream and remaining berries.
Because of the fresh berries, this cake is best eaten the day it is made. It will last, fully made, overnight in the refrigerator (wrap it looselbut the berries, sniff, might weep a bit.