Preheat oven to 350°F (175°C). Grease a 9x13-inch pan and line the bottom with parchment for easy removal.
Whisk flour, baking powder, and salt in a small bowl.
Set aside.
In a large bowl, beat egg yolks with 1/2 cup sugar until pale and thick, about 2–3 minutes. Mix in vanilla and 2 tablespoons milk.
In a clean bowl, beat egg whites to soft peaks. Gradually add the remaining 1/4 cup sugar and beat to glossy medium-stiff peaks.
Fold the dry ingredients into the yolk mixture in two additions.
Gently fold in the whipped whites until just combined. Do not overmix.
Spread batter evenly in the pan. Bake 22–26 minutes, until the top is golden and a toothpick comes out clean.
Cool 10 minutes. Poke holes all over the warm cake with a skewer or fork, going almost to the bottom.
Whisk sweetened condensed milk, evaporated milk, whole milk, and vanilla.
Slowly pour over the cake, letting it absorb. Go in passes so it soaks evenly.
Cover and chill at least 4 hours, preferably overnight, to fully hydrate and set.
Whip cream, powdered sugar, and vanilla to soft-medium peaks. Spread over the chilled cake.
Toss sliced strawberries with a teaspoon of sugar if they’re tart. Spoon over the top.
Brush with thinned strawberry jam if using for a light sheen.
Slice and serve cold. Wipe the knife between cuts for clean squares.