Preheat oven to 350°. Beat butter at medium speed with a heavy-duty electric stand mixer until fluffy; gradually add sugar, beating well. Add egg yolks, 1 at a time, beating just until blended after each addition.
Combine flour and baking powder; stir together milk and coconut milk. Add flour mixture to butter mixture alternately with milk mixture, beginning and ending with flour. Beat at low speed until blended after each addition. Stir in extracts.
Beat egg whites and salt at high speed until stiff peaks form. Stir about one-third egg whites into batter; fold in remaining egg whites. Spoon batter into 3 greased and floured 9-inch round cake pans.
Bake at 350° for 18 to 22 minutes or until a wooden pick inserted in center comes out clean. Cool in pans on wire racks 10 minutes; remove from pans to wire racks, and cool completely.
Place 1 cake layer on a serving platter. Spoon 1/3 cup Vanilla Buttercream into a zip-top plastic bag. Snip 1 corner of bag to make a small hole. Pipe a ring of frosting around cake layer just inside the top edge. Top with half of Ambrosia Filling, and spread to edge of ring. Top with a second cake layer. Repeat procedure with frosting and filling. Top with remaining cake layer, and spread frosting on top and sides of cake.