1. Preheat oven to 350°F. Butter 3 8-inch round cake pans. Line bottoms of pans with parchment paper, then butter parchment. Spoon a small amount of flour into pans, swirl to coat sides and bottom, then tap out and discard excess flour.
2. Make cake: Combine flour, baking powder and salt in a medium bowl. Whisk together milk, egg whites and vanilla in a medium glass measuring cup or bowl.
3. In a large bowl, using an electric mixer on medium-high speed, beat butter and sugar until well combined and light. Reduce speed to low and add 1/3 of flour mixture. Add 1/2 of milk mixture, beating constantly and scraping down sides of bowl as necessary. Beat in another 1/3 of flour, then remaining milk, beating just until blended. Mix in remaining flour just until blended. Divide batter evenly among pans and smooth tops with a rubber spatula (don't worry if batter looks curdled).
4. Bake cakes for 30 to 35 minutes, until a toothpick inserted in center of each cake comes out clean. Transfer cakes to wire racks; cool in pans for 10 minutes. Run a knife around sides of pans, invert cakes onto wire racks and remove parchment. Let cool completely.
5. Make frosting: Beat butter and cream cheese with an electric mixer on medium-high speed in a large, deep bowl until light and fluffy. Reduce speed to low and gradually beat in confectioners' sugar in 2 batches until smooth and creamy. Beat in vanilla just until combined.
6. Assemble cake: Using a serrated knife, gently slice horizontally across top of each cake layer to make level. Place 1 cake layer on serving plate. Spread 1/4 cup jam evenly over layer. Add another cake layer and spread with 1/4 cup jam. Top with final cake layer. Frost top and sides of cake. Cut into wedges and serve.