Preheat oven to 350 degrees. Line a 9x13” pan with foil and spray with cooking spray.
Place the two baking chocolates and butter in a large, microwave safe bowl. Heat on HIGH power for 2-3 minutes, stirring every 30 seconds, until chocolate is smooth. Stir in sugar. Add eggs, vanilla, and cocoa and stir well. Add flour and stir carefully.
Spread batter in prepared pan. Bake about 25 minutes, until a toothpick 2 inches from the outside of the pan comes out clean. Let cool before cutting.
To make the frosting, beat butter in a large bowl with a hand mixer until smooth. Slowly beat in powdered sugar until crumbly. Beat in extract. Add coconut milk, 1 tablespoon at a time, until you reach your desired consistency. Add about 3/4 of the toasted coconut (reserving the rest to sprinkle on top) and stir.
Spread frosting over the top of the cooled brownies. Sprinkle with remaining coconut and slice into squares.