Preheat oven to 350°F (175°C). Grease two 8-inch round cake pans and line bottoms with parchment. Whisk flour, baking powder, baking soda, and salt together.

Beat the softened butter and sugar on medium until pale and fluffy, about 3 minutes. Add eggs one at a time, then beat in lemon zest, vanilla, and lemon juice.

Alternately add flour mixture and buttermilk in three additions, starting and ending with flour, mixing just until combined. Divide batter evenly between pans.

Bake 23 to 26 minutes until golden and a toothpick comes out with moist crumbs. Cool in pans 10 minutes, then turn out onto a rack to cool completely.

In a saucepan over medium heat, whisk lemon juice, sugar, eggs, yolks, and salt constantly until thickened, 4 to 6 minutes. Remove from heat, whisk in butter one cube at a time, then strain into a bowl and chill with plastic wrap on the surface.

Beat cold cream cheese and softened butter until smooth, about 2 minutes. Gradually add powdered sugar, vanilla, and salt; beat until light and fluffy, about 3 minutes.

Place one cake layer on a plate, spread most of the chilled curd on top, then add second layer. Frost top and sides with cream cheese frosting, swirl remaining curd on top, and serve at room temperature.