Step 1
Place a rack in middle of oven and preheat to 350°. Toast 1⅓ cups unsweetened coconut flakes in an even layer on a rimmed baking sheet, stirring halfway through, until golden brown, 6–8 minutes. Let cool.
Step 2
Generously coat a 10”-diameter tube or 15-cup capacity Bundt pan with nonstick vegetable oil spray, making sure to coat every nook and indentation. Sprinkle ¼ cup (50 g) granulated sugar into pan, rotating pan to evenly coat bottom and sides. Sprinkle 1 cup toasted coconut in an even layer in bottom (not sides) of pan. Set remaining coconut aside for serving.
Step 3
Beat 1½ cups (3 sticks) unsalted butter, room temperature, and 8 oz. cream cheese, room temperature, in the bowl of a stand mixer fitted with the paddle attachment, on medium-high speed until almost doubled in volume and very fluffy, about 3 minutes. Turn off motor and add 2½ tsp. Diamond Crystal or 1½ tsp. Morton kosher salt, 1½ tsp. vanilla extract, and 1 tsp. coconut extract. Beat on medium-high speed until mixture is fluffier and similar in texture to frosting, 1–2 minutes.
Step 4
Reduce mixer speed to medium and, with motor running, gradually pour in remaining 3 cups (600 g) granulated sugar in a steady stream, about 2 minutes. Increase speed to medium-high and beat until batter is very pale, incredibly light and fluffy (like whipped butter), and almost tripled in volume, about 5 minutes.
Step 5
Reduce speed to medium and add 6 large eggs, room temperature, one at a time, mixing until each egg is incorporated before adding the next, about 3 minutes total. (Don’t worry if the batter appears slightly broken at this point.) Using a rubber spatula, scrape bottom and sides of bowl.
Step 6
Reduce speed to low speed and add ½ tsp. baking powder, then add 3 cups (375 g) all-purpose flour in 3 batches, mixing after each addition just until flour is barely incorporated before adding more, about 30 seconds per addition. (Some pockets of unincorporated flour are okay.) Gently stir with spatula to incorporate any remaining flour. Dollop batter over coconut in prepared pan and smooth into an even layer, being careful not to mix the coconut and sugar into the batter too much. (Using a cookie scoop to dollop that batter on top of the coconut works well.)
Step 7
Bake cake 40 minutes. Reduce oven temperature to 325° and rotate cake (do not remove from oven). Continue to bake until a tester inserted into the center comes out clean, 45–55 minutes more. Transfer pan to a wire rack and let cake cool in pan 10 minutes. Run a small offset spatula or knife around inside of pan to loosen cake. Invert cake out onto rack and let cool completely.
Step 8
Whisk 2 cups (220 g) powdered sugar and 2 Tbsp. water in a large bowl until smooth. (If glaze is too thick, add an additional 1 tsp. water at a time until thick but pourable.) Pour glaze over cake, allowing it to drip down sides. Immediately scatter reserved coconut over and sprinkle with flaky sea salt if desired. Let sit at least 1 hour before slicing.
Do Ahead: Cake can be made 3 days ahead. Store lightly wrapped at room temperature.