• Preheat oven to 325°F (170°C). Lightly spray 3 (8-inch) round cake pans with baking spray with flour. Line bottom of pans with parchment paper.

Using an Ankarsrum Mixer:

• Assemble Ankarsrum mixer with stainless steel bowl. Place dough knife in smaller hole, and position dough roller just off side of bowl. Add butter; slowly increase mixer speed to medium-high (6 o’clock), and beat until creamy, about 1 minute, using scraper to help move butter around. (Butter might stick to the roller at first.) Slowly add sugars, beating until well combined and lightened in color, about 3 minutes. Add eggs, beating until just combined. Beat in vanilla.
• In a medium bowl, whisk together flours, baking powder, and salt. With mixer on lowest speed (12 o’clock), gradually add flour mixture to butter mixture. Move roller to 1 inch away from side of bowl; increase mixer speed to medium-low (2 o’clock), and beat until combined.
• In a small bowl, whisk together milk and oil. With mixer on low speed (1 o’clock), slowly add milk mixture to batter, beating until combined. Divide batter among prepared pans (about 3 cups or 530 grams each).
• Bake until a wooden pick inserted in center comes out clean and an instant-read thermometer inserted in center registers 200°F (93°C) to 205°F (96°C) , about 45 minutes. Let cool in pans for 10 minutes. Remove from pans, and let cool completely on wire racks.
• Spoon about 1 cup (about 180 grams) Coconut Swiss Meringue Buttercream into a pastry bag, and cut a ½-inch opening in tip.
• Level cooled cake layers if desired. Place 1 cake layer on a serving plate. Spread a very thin layer of buttercream onto cake layer, and pipe a border of buttercream along edge. Spread half of Coconut-Almond Filling (about 1½ cups or 375 grams) within border. Top with second cake layer, and repeat procedure with buttercream and remaining filling. Top with remaining cake layer. Spread a thin layer of buttercream on top and sides of cake. Refrigerate for 30 minutes.
• Spread remaining buttercream on top and sides of cake as desired. Garnish with flaked coconut and chopped almonds, if desired. Refrigerate in an airtight container for up to 3 days.

Using a Conventional Mixer:

• In the bowl of a stand mixer fitted with the paddle attachment, beat butter and sugars at medium speed until light and fluffy, 2 to 3 minutes, stopping to scrape sides of bowl. Add eggs, one at a time, beating until just combined after each addition. Beat in vanilla.
• In a medium bowl, whisk together flours, baking powder, and salt. In a small bowl, whisk together milk and oil. With mixer on low speed, gradually add flour mixture to butter mixture alternately with milk mixture, beginning and ending with flour mixture, beating just until combined after each addition. Divide batter between prepared pans (about 3 cups or 530 grams each).
• Bake until a wooden pick inserted in center comes out clean and an instant-read thermometer inserted in center registers 200°F (93°C) to 205°F (96°C) , about 45 minutes. Let cool in pans for 10 minutes. Remove from pans, and let cool completely on wire racks.
• Spoon about 1 cup (about 180 grams) Coconut Swiss Meringue Buttercream into a pastry bag, and cut a ½-inch opening in tip.
• Level cooled cake layers if desired. Place 1 cake layer on a serving plate. Spread a very thin layer of buttercream onto cake layer, and pipe a border of buttercream along edge. Spread half of Coconut-Almond Filling (about 1½ cups or 375 grams) within border. Top with second cake layer, and repeat procedure with buttercream and remaining filling. Top with remaining cake layer. Spread a thin layer of buttercream on top and sides of cake. Refrigerate for 30 minutes.
• Spread remaining buttercream on top and sides of cake as desired. Garnish with flaked coconut and chopped almonds, if desired. Refrigerate in an airtight container for up to 3 days.