Cook strawberries. Core and quarter 1 1/2 pounds of the strawberries (save the other 1/2 pound for decorating). Place in a large saucepan and place over medium heat. Cook, stirring frequently until strawberries are broken down and the juices have thickened, about 25 minutes. You will know when they are thick enough because when you scrape your spoon along the bottom of the pan it will leave a trail and the juices won't run back on themselves right away. Remove from heat and let cool completely.
Grind strawberries. Place freeze-dried strawberries in the bowl of a food processor fitted with the blade attachment. Pulse 20-30 times or until the strawberries are finely ground without turning into a paste. Measure 1/2 cup of the ground strawberries and save the rest for garnish.
Heat oven. Heat oven to 325°F and arrange a rack in the middle. Grease 2 (8-inch) cake pans and line the bottoms with parchment paper circles. Grease the parchment paper and set pans aside.
Mix dry ingredients. Whisk together all purpose flour, ground strawberries, baking powder, and kosher salt in a medium bowl.
Separate eggs. Gently crack eggs into the bowl of a stand mixer fitted with the whisk attachment. Do this carefully so you don't break the yolks. If you break a yolk you'll have to start over. Gently remove the yolks with your hands, scooping them up and letting the whites run through your fingers. Place yolks in a large bowl—make sure the bowl is big enough to mix all the cake batter eventually. *Once again: important that you don't get any trace of egg yolk in the whites or they won't whip up to stiff peaks. I know this method of separating eggs might sound weird, but it actually is the most gentle way of dividing the yolk from the white.
Beat egg yolks. Add sugar and 1/2 teaspoon of the vanilla to the egg yolks and whisk until thick, creamy, and the sugar is mostly dissolved, about 3 minutes.
Whip egg whites. In the stand mixer, whip the egg whites on medium speed until they are stiff, but not dry, about 6 minutes.
Fold batter together. Add about 1/3 of the egg whites into the yolks and fold gently with a rubber spatula. Add remaining whites and gently fold until only a few largish pieces of egg white remain. Add flour mixture and gently fold that in as well being careful not to deflate the egg whites too much.
Bake. Divide the batter evenly between the two cake pans and bake in the middle of the oven until the top of the cakes are golden around the edges and springy to the touch. A toothpick inserted in the middle should come out clean, about 20-25 minutes.
Make tres leches mixture. While cakes are baking whisk together the sweetened condensed milk, the evaporated milk, and 1/2 cup of the heavy cream in a large bowl.
Cool. Let cakes cool on wire racks for 5 minutes then run a knife around the edge of the cake pans and turn cakes out of the pans onto the wire racks. Remove parchment paper and flip right side up again.
Place on serving dish. Place one cake, top-side-down on a rimmed cake stand or serving platter. Make sure whatever you use has a high rim or the milk mixture will run off the sides. Also make sure your serving plate fits in your refrigerator because it will have to chill for 4 hours.
Soak borttom layer. Poke cake all over with a toothpick then spoon half of the tres leches mixture evenly over the cake. Let a spoonful of the mixture soak in before adding the next and distribute it evenly, don't just dump it in the middle.
Add strawberry filling. Spoon cooked strawberries over the bottom layer of the cake and spread evenly.
Soak top layer. Lay second cake top-side-down on top of the strawberry filling. Press gently to squeeze the filling out to the sides. Poke cake all over with a toothpick and spoon remaining tres leches mixture over the top layer the same as you did with the bottom layer.
Chill. Cover cake and chill in the refrigerator for 4 hours.
Make whipped cream frosting. Right before serving, whip remaining heavy cream and remaining teaspoon of vanilla extract in the bowl of a stand mixer fitted with the whisk attachement on medium-high until it forms big, puffy peaks, about 3 minutes.
Finish decorating. Spoon whipped cream over the top of the cake and spread in swirls to the edge of the cake. Slice remaining 1/2 pound of strawberries in half (I like to leave the stems on if they are pretty). Dust with any leftover ground strawberries if you'd like and serve!