Prep the pan: Heat oven to 350°F (175°C). Grease a 9x13-inch baking pan and line the bottom with parchment for easy slicing.
Mix dry ingredients: Whisk flour, baking powder, and salt in a bowl; set aside.
Beat yolks: In a large bowl, beat egg yolks with 1/2 cup sugar until pale and thick, 2–3 minutes.
Mix in vanilla and 1/4 cup milk.
Whip whites: In a clean bowl, beat egg whites to soft peaks. Gradually add remaining 1/4 cup sugar; beat to glossy medium-stiff peaks.
Fold the batter: Gently fold the dry ingredients into the yolk mixture. Fold in egg whites in three additions, keeping as much air as possible.
Bake: Spread batter in the pan and bake 22–26 minutes, until golden and a toothpick comes out clean.
Cool 15 minutes.
Macerate strawberries: Toss sliced berries with sugar and lemon juice. Let sit 15–30 minutes to release juices.
Make the soak: Stir whole milk, condensed milk, evaporated milk, vanilla, and a pinch of salt until smooth.
Soak the cake: Poke the warm cake all over with a skewer. Slowly pour the milk mixture evenly across the surface.
Let it absorb; chill at least 3 hours, preferably overnight.
Whip the topping: Beat heavy cream, powdered sugar, and vanilla to soft-medium peaks.
Assemble: Spread whipped cream over the chilled cake. Spoon strawberries (with some juices) over the top right before serving.
Serve: Slice into squares. Add extra berries and juice for a little sauce on the plate.