Preheat an oven to 350 degrees F (175 degrees C). Spray an 8x8 inch baking pan with cooking spray, and dust lightly with the 2 tablespoons cocoa powder. Place the coconut in the jar of a blender, and pulse to mince; set aside.
Whisk together the flour, sugar, 1/4 cup cocoa powder, baking powder, and salt. Stir in the brewed chai, canola oil, and vanilla extract, just until all ingredients are moistened. Fold in the coconut. Spread the batter in the prepared pan.
Bake in the preheated oven until the top is no longer shiny, about 20 minutes. Allow to cool for 1 hour before cutting.