White Cake with Swiss Meringue Buttercream

White Cake 

1/2 cup plus 2 tablespoons (1 3/4 sticks) unsalted butter, room temperature, plus more for pans
3 1/2 cups sifted cake flour (not self-rising), plus more for pans
1 tablespoon plus 1 1/2 teaspoons baking powder
1/2 teaspoon salt
2 teaspoons pure vanilla extract
1 1/4 teaspoons whole milk
1 1/2 cups sugar
5 large egg whites, room temperature

1. Preheat oven to 350 degrees F. Butter cake pans, line with parchment. Butter parchment; dust with flour, tapping out excess.

2. Whisk together flour, baking powder and salt in a bowl. Stir vanilla into milk. With an electric mixer on medium speed, beat butter until very smooth, about 2 minutes. With machine running, gradually add sugar; beat until pale and fluffy, 3 to 5 minutes. 

3. With mixer on low speed, add flour mixture in 3 batches, alternating with 2 batches of milk mixture and beginning and ending with flour. Beat until just combined (do not over mix). 

4. In a clean mixing bowl, beat egg whites on medium speed until stiff peaks form, about 3 minutes. Gently fold egg whites into batter in 3 additions. 

5. Divide batter among prepared pans, smoothing tops with an offset aptula. Bake until tops spring back when pressed and a cake tester comes out clean, about 25 minutes for 8-inch round layers. 

Basic Swiss Meringue Buttercream

3/4 cup sugar
3 large egg whites
2 sticks unsalted butter, room temperature
1/2 teaspoon pure vanilla extract
1 drop red food gel
2 drops blue food gel 

1. Place whites and sugar in a heatproof mixer bowl set over a pan of simmering water. Whisk until sugar dissolves (mixture should feel completely smooth when rubbed between your fingers). With an electric mixer on medium speed, whisk egg-white mixture 5 minutes. Increase speed to medium-high, and whisk until stiff, glossy peaks form and meringue has cooled (test by feeling bottom of bowl), about 6 minutes. Reduce speed to medium. Add butter, 1 piece at a time, beating well after each addition. Beat in vanilla and drops of red and blue food coloring. Adjust food coloring until you reach the desired shade of lavender.