Instructions

For the cake: Adjust oven rack to middle position and heat oven to 350 degrees. Grease two 9-inch round cake pans, line with parchment paper, grease parchment, and flour pans. Whisk flour, 2⅓ cups sugar, baking powder, baking soda, and salt together in large bowl. Whisk buttermilk, melted butter, egg yolks, oil, lime zest and juice, and vanilla together in 4-cup liquid measuring cup or medium bowl.
Using stand mixer fitted with whisk attachment, whip egg whites on medium-high speed until foamy, about 45 seconds. Gradually add remaining ⅓ cup sugar; continue to whip until stiff peaks just form, 2 to 3 minutes longer (whites should hold peaks, but mixture should appear moist). Transfer egg white mixture to bowl and set aside.
Transfer flour mixture to clean, dry mixer bowl and fit mixer with clean, dry whisk attachment. With mixer running on low speed, gradually pour in buttermilk mixture and mix until almost incorporated and some streaks of dry flour remain, about 15 seconds. Stop mixer and scrape down bowl and whisk attachment. Mix on medium-low speed until smooth and fully combined, 10 to 15 seconds.
Using rubber spatula, stir one-third of egg white mixture into batter to lighten, then gently fold in remaining egg white mixture until no white streaks remain. Divide batter evenly between prepared pans. Gently tap pans on counter several times to release air bubbles.
Bake until cakes begin to pull away from sides of pans and toothpick inserted in center comes out clean, 40 to 44 minutes. Let cakes cool in pans on wire rack for 10 minutes. Loosen cakes from sides of pans with paring knife, then invert onto greased wire rack and discard parchment. Invert cakes again and let cool completely on rack, about 1½ hours.
For the raspberry curd and mousse: Sprinkle gelatin over water in large bowl and set aside. Whisk egg yolks and cornstarch in medium bowl until combined. Combine raspberries, sugar, butter, and salt in medium saucepan. Lightly mash with whisk and stir until no dry sugar remains. Cook over medium heat, whisking frequently, until mixture is simmering and raspberries are almost completely broken down, 4 to 6 minutes.
Remove saucepan from heat and, whisking constantly, slowly add ½ cup raspberry mixture to yolk mixture to temper. Whisking constantly, return tempered yolk mixture to raspberry mixture in saucepan. Cook over medium heat, whisking constantly, until mixture thickens and bubbles, about 1 minute. Strain mixture through fine-mesh strainer into bowl with gelatin mixture, pressing on solids with back of ladle or rubber spatula until only seeds remain. Discard seeds and stir raspberry mixture until gelatin is dissolved. Let sit, stirring occasionally, until curd is slightly thickened and completely cooled, about 1 hour. Transfer ½ cup curd to small bowl and set aside.
Using stand mixer fitted with whisk attachment, whip cream on medium-low speed until foamy, about 1 minute. Increase speed to high and whip until soft peaks form, 1 to 2 minutes. Transfer one-third of whipped cream to remaining curd and gently whisk until mixture is lightened. Using rubber spatula, gently fold in remaining whipped cream until mixture is homogeneous.
For the frosting: Using stand mixer fitted with whisk attachment, whip butter on medium-high speed until smooth, about 20 seconds. Add sugar and salt; reduce speed to medium-low and whip until most of sugar is moistened, about 45 seconds. Scrape down bowl, add 3/4 cup limeade concentrate and vanilla, and mix on medium-low speed until incorporated, about 45 seconds. Increase speed to medium-high; whip until light and fluffy, about 4 minutes, scraping down bowl as needed. Add green and yellow food coloring and mix until combined.
Using long serrated knife, cut each cake layer in half horizontally. Place 1 cake layer on cake turntable. Brush 3 tablespoons limeade concentrate over top and sides of cake. Spread 1½ cups raspberry mousse evenly over top, leaving ¼-inch border around edge. Top with second cake layer, pressing lightly to adhere. Brush with 3 tablespoons limeade concentrate, then spread with 1½ cups mousse. Top with third cake layer, pressing lightly to adhere. Brush with 3 tablespoons limeade concentrate, then spread with remaining 1½ cups mousse. Top with fourth cake layer, pressing lightly to adhere, and brush with remaining 3 tablespoons limeade concentrate.
Frost top and sides of cake with thin layer of frosting, about 1½ cups, taking care to fill in gaps on sides between layers to create smooth sides. Refrigerate until frosting is firm, 30 to 45 minutes. Frost only sides again with thicker layer of remaining frosting. While turning cake turntable, run small offset spatula vertically from bottom to top of cake at 45-degree angle. Arrange raspberries around top edge of cake (set aside 3 raspberries for center of cake). Spread reserved raspberry curd inside ring of raspberries using offset spatula, covering all exposed frosting on top. Shingle lime slices in center of cake; top with reserved raspberries. Serve.