Preheat oven to 350 degrees F. Line three 8-inch round cake pans with parchment paper. Lightly grease pans and dust with cake flour. Tap out any excess flour. Set aside.
In the bowl of a stand mixer, whisk together cake flour, sugar, malted milk powder, baking powder, salt. Connect paddle attachment to stand mixer. Mixing on low speed, add butter a few tablespoons at a time. Mix on low speed until mixture resembles coarse sand.
In another bowl, whisk together eggs, milk, and vanilla. Add half of mixture to mixing bowl. Mix on low speed until incorporated. Add remaining liquid mixture. Mix until incorporated. Scrape down bowl as needed to ensure thorough mixing. Increase speed and mix until batter is fluffy.
Divide batter among the prepared cake pans. Level off batter. Bake for 22-25 minutes until toothpick inserted in center of cake comes out clean. Allow cakes in cool in pan for 5-8 minutes before unmolding. Allow cake layers to cool to room temperature on wire rack before assembling cake.