Preheat your oven to 350°F (175°C). Grease and flour a bundt pan.
In a medium bowl, whisk together the flour, baking soda, cinnamon, nutmeg, and salt. Set aside.
In a large bowl, beat the butter and sugar together until light and fluffy. Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
Gradually add the flour mixture to the butter mixture, alternating with the sour cream, beginning and ending with the flour mixture. Fold in the chopped apples.
Pour the batter into the prepared bundt pan. Bake for 60 minutes, or until a toothpick inserted into the center comes out clean. Let the cake cool in the pan for 15 minutes, then turn it out onto a wire rack to cool completely.
To make the glaze, whisk together the powdered sugar, milk, and vanilla extract until smooth. Drizzle over the cooled cake.