Heat oven to 350°F. Grease a 13 x 9 x 2-inch baking pan.
Combine butter and chocolate in large microwave-safe bowl. Microwave on HIGH in 30-second increments, stirring, until melted and smooth. Stir in sugar, flour, soda, salt, eggs and vanilla until smooth. Add nuts. Transfer to pan. Smooth until even.
Bake in 350°F oven for 25 minutes.
Meanwhile, combine milk, sugar, butter and egg yolks in 3-quart saucepan. Cook over medium-high heat, whisking, until bubbly, 13 to 15 minutes. Stir in pecans, coconut and vanilla; cook 2 more minutes.
Remove brownie from oven. Pour warm frosting over top of brownie, spreading to edges. Cool 20 minutes at room temperature. Chill 1-1/2 hours or until ready to serve.