Preheat your oven to 350°F and grease a 9x13 inch baking dish. Hull and halve the fresh strawberries, then blend them with the lemon zest until smooth. Let this mixture sit for 30-60 minutes to develop flavor and release its juices. While the strawberries macerate, measure out all your dry ingredients (flour, baking powder, salt) into one bowl and set aside. Ensure your eggs are at room temperature and your heavy cream is well-chilled—these temperature details matter for proper texture in both the cake and the topping.
Blend the macerated strawberry mixture with the 1 cup of strawberry jam until fully combined—this concentrated purée will soak into the cake layers. Separate about 1 cup of this purée to reserve for the three-milk mixture later. Now begin your cake batter: beat the egg whites with cream of tartar until stiff peaks form. In a separate bowl, beat the egg yolks for 3 minutes until pale, then gradually add the granulated sugar and 1 tablespoon vanilla extract, beating until well combined. Gently fold the stiff egg whites into the yolk mixture in two additions to maintain the airiness.
Gently fold the dry ingredient mixture from Step 1 into the egg mixture from Step 2 until just combined—don't overmix, as this keeps the cake light and airy. Pour the batter into your prepared baking dish, then drizzle with 1/2 cup of the strawberry purée and swirl it through using a knife or skewer for visual appeal and flavor variation throughout the cake. Bake at 350°F for exactly 30 minutes until golden and a toothpick inserted in the center comes out clean. I like to tent the pan loosely with foil if the top browns too quickly.
Remove the cake from the oven and immediately poke it all over with a fork to create channels for the milk mixture to absorb. In a bowl, whisk together the sweetened condensed milk, evaporated milk, whole milk, and the remaining 1/2 cup strawberry purée from Step 2. Pour this mixture slowly and evenly over the entire hot cake, allowing it to absorb gradually—this creates the signature soaked texture that defines tres leches. Let the cake cool to room temperature, then refrigerate for at least 2 hours before frosting.
Using well-chilled equipment, beat the cold heavy whipping cream with the powdered sugar and 1 teaspoon vanilla extract until soft peaks form—don't overbeat or you'll end up with butter. Spread this frosting evenly over the chilled cake. Toss the sliced strawberry fans with the 2 tablespoons of melted strawberry jam to create a glossy glaze, then arrange them decoratively on top of the frosting. I find that slicing the strawberries just before plating keeps them looking fresh and prevents excess moisture from making the frosting soggy.