Preheat the oven to 325°F. Grease and flour a 10-cup Bundt pan.
In a large bowl, whisk together flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
In another bowl, combine brown sugar, granulated sugar, vegetable oil, sour cream, eggs, and vanilla extract until well blended.
Add the wet ingredients to the dry ingredients, mixing just until no flour streaks remain. Fold in diced apples and walnuts.
Pour the batter into the prepared Bundt pan. Bake for about 60 minutes, or until a toothpick inserted near the center comes out clean.
While the cake cools, melt butter for glaze in a saucepan over medium heat. Add brown sugar and heavy cream, stirring until the brown sugar dissolves. Remove from heat, stir in powdered sugar, and let thicken.
Drizzle the glaze over the cooled cake.