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