For the cake

1. Adjust oven rack to middle position and heat oven to 350 degrees. Grease and flour four two 9-inch-wide by 2-inch-high round cake pans and line with parchment paper. In 2-cup liquid measure or medium bowl, whisk together milk, egg whites, and vanilla.
2. In bowl of standing mixer fitted with paddle attachment, mix flour, sugar, baking powder, lemon zest, and salt at low speed. With mixer running at low speed, add butter one piece at a time; continue beating until mixture resembles moist crumbs with no visible butter chunks.
3. Add all but 1/2 cup milk mixture to crumbs and beat at medium speed until mixture is pale and combined, about 1 1/2 minutes. With mixer running at low speed, add remaining 1/2 cup milk mixture; increase speed to medium and beat 30 seconds more. Stop mixer and scrape sides of bowl. Return mixer to medium speed and beat 20 seconds longer. Divide batter evenly between cake pans; using rubber spatula, spread batter to pan walls and smooth tops.
4. Bake until toothpick inserted in center of cakes comes out clean, 15-18 minutes. Loosen cakes from sides of pans with small knife, cool in pan 10 minutes, then invert onto greased wire rack; peel off parchment. Invert cakes again; cool completely on rack, about 1 1/2 hours.

For the Lemon Simple Syrup

1. Heat sugar, zest, and water in a small saucepan over medium-high heat, stirring, until sugar has dissolved. Bring to a boil and let boil for 1 minute. Pour through a fine sieve into a medium bowl; discard solids. Let cool completely. Stir in lemon juice.
2. *Extra syrup can be refrigerated, airtight, up to 1 month.

For the Strawberry Lemon Quick Jam

1. If using frozen strawberries, microwave strawberries for one minute to thaw. Place strawberries, sugar, zest, and 1 tablespoon of water in a saucepan. Let cook for about 2 minutes on medium heat until the strawberries start to break down.
2. Using a potato masher or back of a wooden spoon, begin to mash the strawberries into a jam-type consistency. Let simmer for 6-8 minutes or until the jam is a smoother, more broken down consistency.
3. Mix cornstarch with one teaspoon of water and add into the strawberry mixture. Let simmer for about 1 minute, or until the mixture has thickened slightly. Remove from heat and let cool. Stir in 1 tablespoon of lemon juice.

For the frosting

1. In the bowl of an electric mixer fitted with the paddle attachment, whip butter for 8 minutes on medium speed (“4” on a KitchenAid). Butter should become pale and creamy.
2. Add powdered sugar slowly on low speed. Add remaining ingredients except for strawberry puree and freeze dried strawberries (if using) and mix for one minute on low speed, then on medium speed for 6 minute. Frosting will become extremely light, fluffy and creamy.
3. Add strawberry puree and freeze dried strawberry if using and mix until incorporated.
4. Use right away, or refrigerate for up to one day, bringing to room temperature before using.

To Assemble

1. Using a pastry brush, brush lemon simple syrup onto each of the cake layers.
2. Place a cake layer face-up on cake plate or 10″ round thin cake board.
3. Place about 1 cup of frosting on top, and spread evenly with a small offset palette knife.
4. Repeat step 1-2 until one layer remains.
5. Place final layer, face-down (bottom of cake layer is facing up). Place a generous scoop of frosting on top, spreading evenly with an offset palette knife and working your way down the sides until you have a very thin layer of frosting over the entire cake and any holes have been filled. Use a bench scraper to achieve very smooth sides. Chill until set — about 30 minutes.
6. Remove from refrigerator and cover with a final, thicker layer of frosting.
7. Finish with any decorations of choice, or frosting borders. I added a bit more powdered sugar to the remaining frosting to stiffen it up a bit and did a simple piped border around the top and bottom edges of the cake, and topped with decorated skewers (Search Pinterest for cute decorating ideas!).
8. Store in a cake keeper at room temperature for up to 2 days, or in refrigerator for up to 5 days. As with most cakes, it’s best eaten the day it’s made.