Preheat oven to 350°F (175°C). Grease and flour a 9-inch round cake pan or line with parchment paper.
In a medium bowl, whisk together flour, baking powder, baking soda, cinnamon, nutmeg, cloves, and salt.
In a large bowl, beat butter, granulated sugar, and brown sugar until light and fluffy.
Add eggs one at a time, beating well after each addition. Stir in vanilla extract.
Alternately add the flour mixture and sour cream to the butter mixture, starting and ending with flour. Mix until just combined.
Fold in chopped apples.
Pour batter into prepared pan and smooth the top.
Bake 45–50 minutes, or until a toothpick inserted in the center comes out clean.
Cool in pan 15 minutes, then transfer to a wire rack to cool completely.
For frosting, combine butter, brown sugar, and milk in a saucepan. Bring to a boil, stirring constantly, then boil 1 minute.
Remove from heat and cool slightly. Beat in powdered sugar and vanilla until smooth and spreadable.
Spread frosting evenly over cooled cake.