Grease and flour a 10-inch tube pan; set aside.
In a large mixing bowl, beat together granulated sugar and the 1/2 cup butter with an electric mixer until well combined. Beat in eggs and vanilla.
Combine the 2-2/3 cups flour, the baking powder, soda, and salt; add alternately to beaten mixture with buttermilk, beating until combined. Fold in apples.
In a medium bowl, combine brown sugar, nuts, the 1/3 cup flour, and the cinnamon. Mix in the 1/3 cup melted butter.
Place about 2 cups cake batter in the prepared pan, dolloping and spreading evenly. Sprinkle with 1/3 of the crumb mixture (about 1/3 cup). Repeat layers. Bake in a 350 degree F oven for 60 to 70 minutes. Cool for 10 minutes. Remove from pan; cool on wire rack for 30 minutes. Serve warm. Melt chocolate with shortening; drizzle over top. Serves 12 to 16.