Preheat the oven to 350 degrees. Butter and flour two 8-by-3-inch cake pans. In the bowl of an electric mixer using the paddle attachment on medium speed, cream together butter, sugar, and vanilla seeds until light and fluffy, about 3 minutes.
Sift together flour and baking powder. With the mixer on low speed, add the dry ingredients, alternating with milk, starting and ending with flour; scrape down sides twice. Transfer batter to a large bowl.
In the clean bowl of an electric mixer fitted with the whisk attachment, whisk egg whites with pinch of salt on low speed until foamy. Increase speed to high, and continue to whisk until stiff (but not dry) peaks form, 3 to 5 minutes. Whisk one-third of the beaten whites into the batter to lighten the mixture. Using a large rubber spatula, fold remaining whites into the lightened batter. Divide the batter equally among the prepared pans. Bake until golden brown and a cake tester inserted into the cakes comes out clean, 40 to 45 minutes. Remove the pans to a rack to cool for 5 minutes. Invert the cakes onto the wire rack to cool completely.
If cakes are not level, use a serrated knife to trim tops off. Carefully slice each cake horizontally into two equal layers, about 3/4 inch thick. (You will have four layers.) To assemble, place one sliced layer on an 8-inch cardboard cake round. Spread with 1/4-inch of frosting. Repeat with remaining layers, placing the final layer bottom-side up. Lightly coat the assembled cake with a thin layer of frosting to protect against crumbs in the frosting. Finish with remaining frosting. Garnish with candied lemon zest. Serve immediately, or keep refrigerated until ready to serve.