How to Make It
Prepare the Cake Layers: Preheat oven to 350°F. Lightly grease 3 (8-inch) round cake pans with cooking spray. Line bottoms of pans with parchment paper rounds, and spray paper.
Combine butter and sugar in bowl of a heavy-duty stand mixer fitted with paddle attachment. Beat on medium-high speed until creamy and fluffy, 3 to 5 minutes. Stop mixer, and scrape down sides. With mixer running on low speed, add egg whites, 1 at a time, stopping to scrape down sides as needed. Add extracts, beating on low speed just until combined.
Whisk together flour, baking powder, and salt in a bowl. Gradually add flour mixture to egg mixture, alternating with milk, in 3 parts, beginning and ending with flour mixture. Beat until blended after each addition. Divide batter evenly among prepared pans.
Bake in preheated oven until a wooden pick inserted in center comes out clean and edges begin to pull away from pans, 24 to 26 minutes.
Cool Cake Layers in pans on wire racks 15 minutes. Invert onto wire racks, remove pans, and cool completely before frosting, 30 minutes. (Alternatively, wrap in plastic wrap, and freeze 2 hours or refrigerate 4 to 6 hours before frosting.)
Prepare the Vanilla Buttercream: Beat butter in bowl of a heavy-duty stand mixer fitted with paddle attachment on medium speed until creamy, 1 to 2 minutes. Reduce speed to low. With mixer running, gradually add powdered sugar, beating until smooth, about 2 minutes, stopping to scrape down sides as needed. Beat in vanilla and salt. With mixer running on medium speed, gradually add cream, beating until fluffy and spreadable, about 30 seconds.
Place 1 Cake Layer on a serving plate or cake stand. Spoon about half of buttercream into a large 16-inch disposable piping bag. Cut a 1/2-inch opening in tip of bag. Pipe buttercream, 1/3 inch high, in concentric circles starting from the outside and working your way in. Top with second Cake Layer; repeat process, refilling bag as needed. Top with third Cake Layer; repeat process. Generously cover cake with buttercream using an offset spatula. Drag spatula around sides of cake, starting at the bottom. Smooth top of cake
Insert rosemary into top of cake; dust with powdered sugar. Top with cookies.