Preheat the oven to 325°F (163°C).
In a medium bowl, whisk together 3 cups (360 g) all-purpose flour, 2 teaspoons baking powder, and 3/4 teaspoon salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, or in a large bowl with a handheld mixer, beat 1 cup (227 g) unsalted butter (room temperature) and 8 ounces (227 g) full-fat cream cheese (room temperature) on medium speed until smooth and creamy, about 1 minute.
With the mixer running, gradually add 2 cups (397 g) granulated sugar. Increase the speed to medium-high and beat until the mixture is light and fluffy, about 3 minutes. Beat in 2 teaspoons vanilla extract and 3/4 teaspoon coconut extract.
Reduce the mixer speed to medium-low. Add 5 large eggs (room temperature) one at a time, beating well after each addition and scraping down the sides and bottom of the bowl as needed.
Add 1/2 cup (113 ml) Thai Kitchen (or similar) unsweetened coconut milk (stir or shake the can well before measuring if necessary) and 1/4 cup (57 ml) unrefined coconut oil (melted and slightly cooled). Beat just until incorporated.
Reduce the speed to low and add the flour mixture in two additions, mixing just until combined. Do not overmix.
Generously grease a 10-inch (12-cup) bundt pan, making sure to coat all nooks and crannies (a non-stick baking spray with flour or butter plus a light dusting of flour works well).
Scrape the batter into the prepared pan and smooth the top with a spatula.
Bake for 55 to 60 minutes, or until the cake is golden brown and a toothpick inserted into the center comes out clean. Remove from the oven.
Let the cake cool in the pan on a wire rack for 10 minutes. Then invert the cake onto the rack and let it cool completely, about 2 1/2 hours.
While the cake cools, melt 4 ounces (170 g) quality white chocolate (use a double boiler or short bursts in the microwave, stirring frequently). Allow the melted white chocolate to cool for 10 minutes.
Make the frosting: In the bowl of a stand mixer fitted with the paddle attachment, or in a large bowl with a handheld mixer, beat the remaining 1 cup (227 g) unsalted butter (room temperature) on medium speed until completely smooth. Reduce the speed to low and gradually add 2 1/2 cups (283 g) sifted confectioners' sugar, beating until incorporated.
Add 1/4 teaspoon salt, 3 and 1/2 Tablespoons (49 ml) Thai Kitchen (or similar) unsweetened coconut milk (stir or shake the can well before measuring if necessary), and 1/4 teaspoon coconut extract. Beat until smooth. Add the cooled melted white chocolate and beat until the frosting is smooth. Increase the speed to medium-high and beat for 1 minute to lighten the frosting.
Spread the frosting evenly over the top and sides of the completely cooled cake. Press 2 cups coconut (sweetened shredded, finely shredded, or flaked) onto the frosting to coat the entire cake.
Allow the frosting to set for 20 minutes, then slice and serve.