Place the strawberries in a microwave safe bowl. Cover and microwave until the strawberries are soft and have released their juice, about 5 minutes stirring halfway through. Press the mixture through a fine-mesh sieve set over a 3 quart saucepan. Firmly press the fruit dry using the back of a spoon. Reserve and refrigerate the strawberry solids for the frosting.

Stir together the lemon juice and cornstarch. Add to the saucepan along with the sugar. Bring the juice to a boil over medium heat and cook stirring constantly for 1 minute. Remove from the heat and place a piece of plastic wrap directly on the warm jam. Chill 2 hours or until cold. Refrigerate for up to 1 week.

In a small food processor combine the lemon zest with 1/4 cup of granulated sugar. Process until the sugar is bright yellow and moist. If you don’t have a food processor combine the sugar and zest in a bowl and blend with your fingers until the zest is broken down and the sugar is bright yellow. You can also muddle the mixture using a mortar and pestle. Set aside.

Whisk the milk, lemon juice, egg whites and vanilla together; set aside.

Using a stand mixer fitted with the paddle attachment combine the flour, all remaining granulated sugar, lemon sugar, baking powder and salt on low until blended. With the mixer running on medium add the butter, 1 piece at a time, and continue mixing until only pea-size pieces remain.

Pour in half the egg white mixture and increase the speed to medium-high. Beat until the mixture is light and fluffy, about 1 minute. Reduce the speed to medium-low and add the remaining egg white mixture. Blend again until combined. The batter may look slightly curdled; this is okay. Stir the batter a few times by hand using a spatula scraping the bottom and sides of the bowl until well blended. Do not overmix.

Divide the batter between the three prepared pans and smooth the tops. Bake until the tops are lightly browned and a toothpick comes out clean, about 18 to 22 minutes. Rotate the pans halfway through baking and don’t over-bake.

Cool the cakes in the pans for 10 minutes the remove and discard the parchment. Cool completely on a wire rack before frosting.

Using an electric or stand mixer beat the butter and cream cheese until smooth, about 30 seconds. Add half the powdered sugar, half the reserved strawberry solids and salt. Blend on medium-low until most of the sugar is incorporated. Scrape down the sides and bottom of the bowl and blend again.

Place one cake layer on a plate or cake stand. Pipe a border of frosting around the outside edge of the cake to create a wall. Fill the center with half the strawberry filling. Add another cake layer and repeat with a frosting border and filling. Top with the final layer of cake. Frost the sides and top of the cake smoothing and/or decorating as desired.

Cake can be refrigerated for 2 days. Bring to room temperature before serving.