Adjust oven rack to middle position and heat oven to 350°F. Grease 16-cup tube pan.
Combine flour, baking powder, baking soda, salt, cinnamon, and nutmeg in medium bowl. Set aside
With electric mixer on medium-high speed, beat granulated sugar, oil, eggs, and vanilla until thick and glossy, about 2 minutes. Stir in apple sauce.
Reduce speed to low and slowly add flour mixture until incorporated, about 1 minute. Using rubber spatula, fold in apples and nuts.
Pour batter into prepared pan and bake until toothpick inserted into center comes out clean, 60 to 75 minutes. Let cool in pan 10 minutes, remove cake from pan onto wire rack, and let cool completely (at least two hours).
For the Topping: Heat butter, brown sugar, and milk in small saucepan over medium heat until thick and syrupy, about 2 minutes. Cool slightly and pour over cooled cake. Allow glaze to set for about 25 minutes before serving.