Heat oven to 350°F (175°C). Grease and flour a 9-inch round cake pan or springform pan.
In a bowl, whisk flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
In another bowl, cream butter and sugar until fluffy. Add eggs and vanilla, then mix in sour cream.
Alternate adding flour mixture and milk until smooth.
Gently stir diced apples into batter.
Pour into pan, smoothing top. Bake 40–45 minutes, or until golden and a toothpick inserted in center comes out clean.
Let cool slightly. Dust with powdered sugar and slice into wedges.