Preheat the oven to 350 degrees F (175 degrees C). Grease two 9-inch round baking pans.

Stir flour, baking powder, and salt together in a medium mixing bowl.

Heat milk and butter in a medium saucepan over low heat until milk is hot and butter is melted, about 5 minutes. Remove from heat.

Beat sugar, eggs, and vanilla extract in a large mixing bowl with an electric mixer on medium speed until thickened and lightened in color. Reduce speed to low. Gradually add flour mixture and beat until blended. Slowly pour in hot milk mixture and beat until combined.

Divide batter evenly between the baking pans.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 30 minutes. Cool cakes in the pans for 10 minutes. Invert onto cooling racks to cool completely, about 15 minutes more.

Make frosting while cakes are cooling. Beat cream cheese and butter with an electric mixer on medium speed until smooth. Add powdered sugar gradually on low speed. Add lemon zest and vanilla extract and beat until smooth.

Carefully split each cooled cake in half horizontally. Spread lemon curd between each layer. Spread cream cheese frosting over the top and sides.