Preheat oven to 350 degrees. Grease and flour a 9x13-inch pan.
BROWNIES: In a medium bowl, combine flour, cocoa powder, baking powder and salt; set aside.
In a large bowl, using a wood spoon, stir the sugar, melted butter, and vanilla together.
In a small bowl, lightly beat the eggs, and stir into the melted butter mixture.
Gradually add flour mixture to the egg mixture, stir until just combined. Spread the batter evenly into the prepared baking dish.
Bake for 25 to 30 minutes or until a tooth pick inserted into the middle comes out clean. Do not overcook. Remove from the oven, cool pan on wire rack. Cool brownies completely before frosting.
FROSTING: Combine milk, sugar, eggs, butter and vanilla in a saucepan. Cook and stir over medium heat until thickened, about 12 minutes.
Remove from the heat and add coconut and pecans. Cool, stirring occasionally, until you've reached spreading consistency. Frost the cooled brownies. Cut the brownies into squares with a plastic knife and refrigerate until ready to serve.