Grease and flour a standard 8-inch Bundt pan with butter and a light dusting of flour, ensuring all crevices are coated. Preheat the oven to 350°F (180°C).
In a medium-sized bowl, whisk together the flour, baking powder, and salt until thoroughly combined. Set aside.
In a large mixing bowl, cream the softened butter and sugar together until the mixture becomes light in color and airy in texture.
Incorporate the eggs one by one, followed by the yolks, beating gently after each addition to ensure full integration. Stir in the coconut cream, coconut extract, and vanilla extract until the batter is uniform and smooth.
Add the dry mixture in three parts to the wet batter, mixing just until each portion is combined. Scrape down the bowl as needed. Carefully fold in the chopped white chocolate with a spatula, being mindful not to deflate the batter, which will be airy and pale.
Transfer the batter evenly into the prepared Bundt pan and level the surface using a spatula. Bake for 40–45 minutes or until a skewer inserted into the center emerges with a few moist crumbs attached. Cool the cake in the pan for 10 minutes, then invert onto a serving plate to cool completely.
While the cake cools, prepare the frosting. Beat the cream cheese with the powdered sugar and coconut extract until smooth. Gradually add the milk or coconut cream, one tablespoon at a time, until the glaze reaches a thick but pourable consistency.
Once the cake has reached room temperature, pour the glaze over the top, using a spatula or spoon to spread it evenly along the surface and sides.
Sprinkle with both shredded coconut and flaked coconut, gently pressing so the toppings adhere to the glaze.