Preheat oven to 350 degrees. Butter two 8-inch round cake pans and line bottoms with parchment; butter parchment as well. Whisk together flour, baking powder, and salt. Beat together butter and granulated sugar with a mixer on medium speed until combined, 1 to 2 minutes. Add eggs and beat well, scraping down sides of bowl as necessary. Reduce speed to low and gradually add flour mixture, beating until combined. Add milk and vanilla and beat until just combined.

Divide batter between pans; smooth tops with an offset spatula. Bake until golden and a toothpick inserted into centers comes out clean, 33 to 35 minutes. Let cakes cool in pans on wire racks 15 minutes. Turn out cakes onto racks to cool completely.

Beat together butter and cream cheese with a mixer on medium-high speed until pale and creamy, about 1 minute. Reduce speed to medium. Add confectioner's sugar, 1 cup at a time, beating well after each addition. Add salt, milk, and vanilla and beat until fluffy, about 3 minutes. If not using immediately, cover surface of frosting with plastic wrap. Frosting can be refrigerated in an airtight container up to 1 week. Before using, bring to room temperature, then beat on low speed until smooth.

Place 1 cake layer on a cake plate and spread 1 cup frosting on top. Place remaining cake layer on top. Spread top and sides of cake with remaining frosting, swirling to coat in a decorative fashion. (If frosting becomes too soft, refrigerate to firm up.) Cake can be covered with a cake dome and refrigerated overnight. Bring cake to room temperature before serving.