Preheat oven to 350°F (175°C). Grease three 8-inch cake pans, line with parchment, and grease parchment. Cream 3/4 cup butter and sugar for 4 minutes until light and fluffy.

Beat in eggs one at a time, then vanilla and coconut extract. Whisk flour, baking powder, and salt. Add dry ingredients in three additions alternating with coconut milk in two, mixing just until smooth. Fold in 1 cup shredded coconut.

Divide batter among pans. Bake 22 to 25 minutes until golden and a toothpick comes out with moist crumbs. Cool 10 minutes in pans, then turn out and cool completely.

Beat cold cream cheese and 1/2 cup butter until smooth. Gradually add powdered sugar, then vanilla and coconut extract, whipping until creamy.

Place one layer on a plate, spread 3/4 cup frosting. Repeat with second and third layers. Apply a thin crumb coat and chill 20 minutes. Frost top and sides with remaining frosting. Toast 2 cups shredded coconut in a dry skillet for about 4 minutes until golden, stirring often. Press onto the sides of the cake and serve.