Preheat ovent to 375. Line a 9x5 inch loaf pan with parchment paper. Set aside.
In a mixing bowl, sift the flour, baking powder and salt.
In a stand mixer or using a hand mixer, add your butter and sugars and beat on medium speed for 5 minutes until the mixture is light and creamy.
Add the eggs one at a time, beating well after each addition. Scrape down sides of the bowl as needed.
Add the vanilla extract and mix.
Alternating between the flour mixture and the coconut milk, add each in three additions ending with the flour.
Fold in the 1 1/2 cups of the shredded coconut.
Pour the batter into prepared loaf pan and bake in the oven for 60 - 70 minutes or until a toothpick inserted into the center comes out clean.
Remove loaf from oven and allow to cool for 10 minutes. Remove loaf from pan and allow to completely cool on a wire rack. Combine powdered sugar and reserved coconut milk. Drizzle over top of loaf and sprinkle with remaining coconut.