Instructions

1. Place 2 cups whole milk and 1/3 cup of the granulated sugar in a large saucepan. Bring to a boil over medium heat, stirring to dissolve the sugar. Meanwhile, place the remaining 1/3 cup granulated sugar and 6 large egg yolks in a medium bowl and whisk until pale in color and fluffy.
2. When the milk just comes to a boil, reduce the heat to maintain a very low simmer. Sprinkle in 3/4 teaspoon cornstarch into the egg mixture and whisk vigorously until smooth and no lumps remain.
3. Transfer 1/2 cup of the milk into the egg mixture and whisk until incorporated. Pour the remaining milk into the eggs and whisk to combine. Pour everything through a fine-mesh strainer back into the saucepan. Discard the contents of the strainer.
4. Increase the heat to medium, whisking constantly. When the mixture becomes too thick to whisk, switch to a heatproof spatula and continue to cook, stirring constantly and scraping down the sides of the saucepan as needed, until the mixture simmers, thickens enough to coat the back of a spoon, and reaches 185ºF, 4 to 6 minutes.
5. Remove the pan from the heat. Add 1 tablespoon unsalted butter and stir until melted and combined. Add 1 tablespoon vanilla bean paste and 1 teaspoon kosher salt and stir to combine.
6. Transfer to a medium bowl. Press a sheet of plastic wrap directly onto the custard to prevent a skin from forming. Let cool 10 minutes at room temperature, then refrigerate until completely chilled, at least 2 hours or up to overnight. Meanwhile, make the cake.
7. Place 2 large egg whites in the bowl of a stand mixer (or in a large bowl if using an electric hand mixer). Place 3 large eggs, 3 sticks unsalted butter, and 1 1/2 cups buttermilk on the counter and let sit at room temperature until the butter is softened.
8. Arrange a rack in the middle of the oven and heat the oven to 350ºF. Line 3 (9-inch) round cake pans with parchment paper rounds, then coat with cooking spray. If you don’t have 3 pans, plan to bake the cakes in rounds instead.
9. Place 3 2/3 cups cake flour, 2 teaspoons baking powder, 1 teaspoon kosher salt, and 3/4 teaspoon baking soda in a large bowl and whisk to combine.
10. Add 1/4 cup of the granulated sugar to the egg whites and beat with the whisk attachment on medium speed until stiff peaks form, about 2 minutes. Transfer the beaten egg whites to a medium bowl. Wash and dry the stand mixer bowl.
11. Add the softened butter and remaining 1 1/4 cups granulated sugar to the stand mixer. Beat with the paddle attachment on medium-high speed until pale and fluffy, stopping and scraping down the sides of the bowl as needed, 3 to 5 minutes. Beat in the 3 large eggs one at a time, waiting until each egg is incorporated before adding the next.
12. Add 1 tablespoon vanilla bean paste and 2 teaspoons finely grated lemon zest and beat until just combined. Add the flour mixture and beat on low speed until just barely combined. With the mixer on low speed, pour in the buttermilk and mix until just combined, about 15 seconds. Turn off the mixer. Fold in the beaten egg whites by hand with a rubber spatula in four additions.
13. Divide the batter into the cake pans, about 2 1/3 cups per pan. Bake until a toothpick or tester inserted in the center comes out clean, 23 to 26 minutes. Let cool at least 30 minutes. Meanwhile, prepare the strawberries.
14. Trim 1 pound strawberries. Thinly slice 3 for garnish and refrigerate. Quarter the remaining strawberries and place in a large bowl. Pick and set aside any blossoms from 1 small handful Thai basil sprigs for garnish. Pick the leaves and finely chop until you have 1 tablespoon. Pick the leaves from 1 small handful fresh mint sprigs, then finely chop until you have 1 tablespoon. Add the chopped basil and mint to the bowl.
15. Add 1 tablespoon lemon juice, 2 teaspoons dry gin, and 1/2 teaspoon ground cardamom, and stir to combine. Let sit at least 20 minutes at room temperature or refrigerate overnight.
16. Remove the cakes from the pans and discard the parchment. Using a serrated knife, trim the domed tops from the cakes so that they are level.
17. Place 1 cup cold heavy cream in a large bowl and beat with a whisk until stiff peaks form, about 2 minutes. Add half of the custard to the whipped cream and gently fold to combine.
18. Place one cake layer on a serving platter or cake plate. Spread half of the remaining custard onto the cake. Spoon 1/2 of the strawberries onto the custard in an even layer. Stack the second cake layer on the strawberries, then repeat spreading on the remaining custard and adding the remaining strawberries. Top with the third cake layer.
19. Frost top and sides of the cake with the whipped cream-custard mixture. Decorate with the thinly sliced strawberries and reserved Thai basil blossoms.