Cake Preheat oven to 350F. Grease and flour a 10-12-cup Bundt pan. In a medium bowl, whisk together flour, baking powder, and salt. Using an electric mixer, beat butter on medium speed until light and fluffy, about 3 minutes. Scrape down sides of bowl, then add eggs and yolks one at a time, beating well after each addition. Scrape down bowl again, add coconut and vanillas, and beat until just incorporated.

Add flour mixture in three parts, alternating with coconut milk, beginning and ending with flour mixture, mixing after each addition until just combined; do not overmix. Spoon batter into prepared pan, smoothing top into an even layer. Bake until a toothpick inserted in center comes out with just a few moist crumbs, 50-55 minutes. Transfer pan to a wire rack to cool completely. Gently loosen sides of cake from pan and turn out onto rack.

Coconut Glaze In a large bowl, whisk together 4 Tbsp of coconut milk, coconut extract, and vanilla. Add powdered sugar and whisk until smooth. Slowly stir in white chocolate. The glaze should be thick yet pourable; if the glaze appears too thick, thin with additional coconut milk, a Tbsp at a time, until desired consistency.

Pour glaze in large, thick ribbons over crown of the cake, allowing glaze to spread and drip down the sides. Top with toasted shredded coconut immediately and allow glaze to set before serving, about 5 minutes. The cake can be kept in an airtight container at room temperature for up to 3 days.