In a medium bowl stir together the flour, baking powder, salt, nutmeg, cinnamon, and baking soda; set aside.
In a very large mixing bowl beat butter with an electric mixer on medium to high for 30 seconds. Gradually add the 2 cups sugar, about 1/4 cup at a time, beating on medium until well combined. Scrape sides of bowl; beat for 2 minutes more. Add eggs, one at a time, beating well after each addition. Add flour mixture to butter mixture, beating on low just until combined. Fold in apples and walnuts. (Batter will be thick.)
Spread batter in a greased 3-quart rectangular baking dish. Bake in a preheated 350º oven for 45 to 50 minutes or until a toothpick inserted near the center comes out clean. Cool in pan on a wire rack for 45 minutes.
Meanwhile, in a small saucepan melt the 1/3 cup butter over medium heat. Stir in the 1/3 cup sugar, brown sugar, and whipping cream. Bring to boiling, stirring constantly. Remove from heat; stir in vanilla. Serve warm.