3/4 cup unsalted butter, room temperature, plus more for pan
2 cups all-purpose flour (spooned and leveled), plus more for pan
1 1/2 teaspoons baking powder
1/2 teaspoon fine salt
1 cup granulated sugar
1 teaspoon pure vanilla extract
3 large eggs
1 cup plus 2 tablespoons buttermilk, divided
1 1/2 cups sweetened shredded coconut, toasted, divided
1 cup confectioners' sugar
Preheat oven to 350 degrees. Grease and flour a loaf pan. Whisk together flour, baking powder, and salt. In a large mixing bowl with paddle attachment, beat butter and granulated sugar on medium-high until light and fluffy, scraping down bowl as needed. Add vanilla, then eggs, one at a time, beating well and scraping down bowl. With mixer on low, add flour mixture in 3 additions, alternating with two 1/2-cup additions buttermilk, and beat until combined. With a rubber spatula, fold in 1 1/4 cups coconut.
Transfer batter to pan and bake until a toothpick inserted in center comes out with a few moist crumbs attached, 60 minutes. Let cool in pan the remove cake from pan and let cool completely on rack.
Whisk together confectioners' sugar and remaining 2 tablespoons buttermilk. Drizzle over cake and sprinkle with remaining 1/4 cup coconut.