Preheat oven to 410°F (210°C) and line a 15x11-inch rimmed baking sheet with parchment paper.
In the bowl of a stand mixer fitted with the whisk attachment, beat eggs, sugar, and vanilla on medium-high speed until thick and pale and has tripled in volume, about 8-10 minutes.
In a small bowl combine flour, salt, and baking powder.
In three additions, sift flour mixture into egg mixture, folding to combine after each addition.
Transfer batter to the prepared baking sheet and smooth the top with an offset spatula. Bake until light golden brown, about 10 minutes.
Dust a clean kitchen towel generously with powdered sugar and Invert the cake onto it; slowly remove the parchment paper. You can brush the paper with a little bit of water to make it easier to peel off.
Using the towel and starting at a short end, roll up the cake and towel. Let cool completely, seam side down.
When the cake has cooled, make the strawberry filling.
Using a handheld immersion blender or food processor puree the strawberries. You should have about 1/2 cup strawberry puree.
In a small saucepan reduce the puree by half. Let cool.
In the bowl of a stand mixer fitted with the paddle attachment beat butter and sugar at medium speed until pale and fluffy.
Add cream cheese and mix until the mixture is whipped, white and fluffy, about 1-2 minutes. Scrape down the bowl as needed.
Add the strawberry puree and stir into the mixture on low speed until just fully incorporated.
Carefully unroll the cake. Spread strawberry filling evenly over the surface, leaving a 1/2-inch border on the outer short end. Gently roll up the cake tightly in the same direction you rolled it the first time (without the towel).
Place it on a serving platter and cut off the ends for a prettier cake if desired.
To garnish, beat together 1/2 cup heavy cream with 1 tbsp powdered sugar on high speed until whipped.
Garnish the cake with dollops of whipped cream and strawberries.