Gather all ingredients.

Preheat the oven to 350 degrees F (175 degrees C). Lightly spray a 13- x 9-inch baking dish with baking spray; set aside.

Whisk together flour, baking powder, and salt in a bowl. In the bowl of a stand mixer fitted with a paddle attachment, beat eggs, sugar, and vanilla on medium speed until light, fluffy, and almost doubled in volume, about 10 minutes.

Beat in half of the flour mixture on low speed until just incorporated. Gradually stream in the milk until combined, followed by the remaining flour mixture. Transfer batter to prepared baking dish.

Bake in preheated oven until golden brown and a wooden skewer inserted in the center of the cake comes out clean, 25 to 30 minutes. Remove from oven and allow to cool on a wire rack in the pan for 20 minutes.

Meanwhile, for the strawberry milk, toss strawberries and sugar in a small bowl until fully coated; let rest at room temperature for 10 minutes, stirring occasionally. Transfer to a blender and process until smooth, about 30 seconds. Strain puree through a fine mesh sieve into a large bowl, discarding any pulp or seeds. Whisk together 1 cup of the strained strawberry puree, evaporated milk, condensed milk, and heavy cream into a large bowl until fully combined.

Using a wooden skewer or the tines of a fork, poke holes all over the top of the cooled cake; pour strawberry milk mixture evenly over cake. Cover with plastic wrap and refrigerate for at least 4 hours or up to 12 hours.