Combine fresh strawberries and two tablespoons of sugar in a blender. Pulse until strawberries are reduced to a pulp. DO NOT blend until smooth. (You will use 1/2 cup of the puree for the cake. Reserve the remaining puree to use in the frosting.) Set aside and allow to macerate further while you perform next few steps.
Make the Cake Layers
Preheat oven to 350°F [175°C]. Grease and flour three 9-inch round cake pans.
Whip eggs whites until they form medium peaks. Set aside.
Combine sifted flour and baking powder. Set aside.
Whisk together milk, strawberry puree, lemon zest, and vanilla. Set aside.
In a large mixing bowl, cream together butter, sugar, dry strawberry Jell-O®, and salt. Beat in eggs yolks one at a time.
Stir flour mixture into batter alternately with strawberry-milk mixture.
Gently fold in whipped egg whites.
Pour batter evenly into the three prepared cake pans. Bake in preheated oven for 20-25 minutes, or until a toothpick or skewer comes out clean.
Allow cakes to cool in their pans over wire rack for at least 10 minutes. Carefully tap out onto wire rack to cool completely.
Make Strawberry Frosting
Using an electric mixer, beat butter on medium-high until light and fluffy.
With mixer on low, add powdered sugar to the whipped butter alternately with 1/3 cup pureed strawberries. Combine thoroughly into a soft, creamy mixture that will hold its shape. Cool in the refrigerator for 10 minutes, or until it has firmed up slightly.
Assemble the Cake
Spread the top of the bottom layer of cake with frosting. Add the middle layer and refrigerate again until the frosting has firmed up a bit. Add the top layer and frost sides and top of cake. For a cleaner frosting, apply a crumb coat first to keep the crumbs out of your final frosting. If you are spreading the frosting on thick, you may want to refrigerate the cake after you apply the frosting between each layer until the frosting has firmed just a bit; about 10-15 minutes for each layer. (If you are frosting it thin, you probably won't need to do this.)
This website provides approximate nutrition information for convenience and as a courtesy only. You are solely responsible for ensuring that any nutritional information provided is accurate, complete, and useful.