Preheat oven to 350°F (180ºC). In large bowl, whisk together flour, baking powder and salt. Set aside. In separate bowl, with hand-mixer, beat butter and sugar until light and fluffy. Beat in eggs, one at a time, until incorporated after each addition. Beat in banana and vanilla. With mixer on low, alternately add the flour mixture in 3 parts with coconut milk in 2 parts, starting and ending with flour mixture. Scrape the bowl as needed between additions. Fold in coconut. Scrape into two greased and floured or parchment paper-lined 9-in (23-cm) round cake pans; smooth top.
Bake 35 to 40 min. or until a cake tester comes out clean when inserted into centre. Cool cake in pans on wire racks 30 min. Remove from pans and cool cakes completely on racks, about 10 min.
Meanwhile, to make frosting, in heatproof bowl, beat water, sugar, egg whites, corn syrup, cream of tartar and salt with hand-mixer on high 1 min. Set bowl over saucepan of simmering water (do not let bottom of bowl touch water. Beat 7 min. or until mixture holds stiff peaks. Remove from saucepan. Continue to beat 2 to 3 min. or until frosting is cooled and thick enough to spread. Beat in vanilla.
Place first cake on platter and spread with about 1 cup (250 mL) frosting. Top with second cake. Ice top and sides with remaining frosting. Sprinkle top of cake with toasted coconut. Refrigerate until ready to serve.
Cakes can be made a day ahead. Wrap and store in airtight container or re-sealable bag. Make frosting on same day as serving.