Preheat oven to 350°F.
In a medium bowl, measure 3/4 cup + 2 tbsp white granulated sugar. Add zest of 1 lemon and massage zest into sugar thoroughly.
Cream 12 tbsp unsalted butter, softened, in a stand mixer on medium speed with the lemon-infused sugar.
Add 2 eggs, one at a time, while mixing on low-medium speed.
Once fluffy, add your 1/2 cup sour cream, 3/4 cup light cream, and 1/3 cup lemon juice. Turn mixer off once combined.
In a large bowl, sift together 1 1/4 cups AP flour, 3/4 tsp baking powder, 3/4 tsp baking soda, and 1 1/4 tsp kosher salt.
Add your sifted dry ingredients to the wet ingredients gradually, in 2-3 batches, folding with a spatula until no streaks remain.
Line a large sheet pan with parchment paper and spray lightly with cooking spray. Spread your cake batter evenly on the full sheet tray.
Bake for 20-25 minutes until cake is lightly golden brown and springs back when touched. Carefully remove cake on parchment from pan and let cool.
To make curd, combine 5 eggs, 3/4 cup white granulated sugar, the zest of 3 lemons, 1 tbsp cornstarch, 1/2 tsp kosher salt, and 1 cup of lemon juice in a large saucepan.
Cook over medium heat, stirring constantly with a whisk, until the curd is thick and pudding-like, about 5-10 minutes.
Remove curd from heat and add gelatin (pre-bloomed in cold water), and 12 tbsp unsalted butter, chopped into small pieces. Whisk until smooth and combined.
Transfer curd to a heatproof bowl and cover with plastic wrap, adhering directly to the surface of the curd. Chill for at least 2-3 hours.
Once cake is rested but still slightly warm, wrap in plastic wrap if you're not using until the next day. You can chill the curd overnight and make the frosting anytime.
To make the frosting, blend 3/4 cup white granulated sugar with 1 cup fresh basil in a blender or food processor.
Combine basil sugar with 4 egg whites in the (clean) bowl of a stand mixer. Place over a double-boiler on medium-high heat and whisk constantly to dissolve sugar, for about 5 minutes.
Transfer stand mixer bowl to stand mixer and mix with the whisk attachment on high for 5 minutes until a meringue with stiff peaks forms.
Turn mixer speed down to medium-low and gradually add 14 tbsp unsalted butter, softened, incorporating each piece fully into the meringue.
Transfer your fluffy meringue frosting into a piping bag and place in the fridge until ready to use.
Cut your sheet cake into 3 long rectangles, measuring the width of the cake with a ruler to ensure evenness. Then, cut each of the 3 long rectangles in half to make shorter rectangles.
Remove lemon curd from fridge and whip with a whisk or in the stand mixer until fluffy.
Spread a large dollop of curd onto the first piece of cake and spread evenly. Place another cake piece on top and repeat 5 times until the cake is assembled, ending with your last cake piece.
Use remaining curd to spread a crumb coat around the exterior of the cake. Place in fridge for at least 30 minutes to 1 hour to firm up.
Slice cake into 8 equal pieces (about 1.5" thick) and place each on a baking sheet with the layers exposed. Pipe a large dollop of basil frosting onto each slice and garnish with basil leaves and lemon slices.