Preheat oven to 350 degrees.
Grease and Flour 13x9inch baking pan.
In a large bowl combine flour, sugar, brown sugar, baking powder, baking soda and nutmeg.
Add milk, butter, eggs, and vanilla.
Beat with a mixer on low until combined. Beat on medium for one minute. Pour batter into the prepared pan.
Bake for 25-30 minutes or until toothpick inserted in center comes out clean.
While cake is baking prepare frosting by adding butter, coconut, brown sugar and milk in a small saucepan.
Cook and stir over medium heat until thick and bubbly. Stir in chopped and toasted walnuts.
Spoon topping over hot cake.
Cool cake in pan on wire rack.