Slice 2 pounds of strawberries and set them aside. In a medium saucepan, combine the water, sugar, cornstarch, and salt. Cook over medium heat, stirring constantly until the cornstarch fully dissolves. Add the sliced strawberries and continue to cook for 5–7 minutes, or until the mixture thickens and the strawberries soften.

Remove the saucepan from heat and stir in the lemon juice. Let the strawberry filling cool to room temperature. Set aside the remaining ½ pound of whole strawberries to use later when assembling the cake.

Preheat the oven to 350°F (175°C). Grease and flour two 8- or 9-inch round cake pans, or line them with parchment paper. In a medium bowl, whisk together the flour, cornstarch, baking powder, and salt, then set the dry mixture aside.

In a large mixing bowl, beat the softened butter and sugar together using an electric mixer until the mixture is light and fluffy, about 3–4 minutes. Add the egg whites one at a time, beating well after each addition. Mix in the vanilla extract.

With the mixer on low speed, alternately add the dry ingredients with the milk and oil, beginning and ending with the dry mixture. Mix until just combined—do not over mix to keep the cake tender.

Evenly divide the batter between the prepared pans. Bake for 25–30 minutes, or until a toothpick inserted into the center comes out clean. Let the cakes cool in their pans for 10 minutes, then transfer to a wire rack to cool completely.

To make the frosting, beat the butter until smooth and creamy. Gradually add the powdered sugar, vanilla, and 1 tablespoon of milk or cream. Continue beating on high speed until the frosting is fluffy, adding more milk if needed for a spreadable consistency.

To assemble the cake, place one cake layer on a serving plate. Spread half of the strawberry filling over the top, then layer some of the reserved whole strawberries. Place the second cake layer on top and frost the entire cake with the vanilla buttercream. Decorate with additional fresh strawberries as desired.