Heat oven to 350°F. Line a 12-cup muffin pan with paper liners.
Whisk flour, baking powder, baking soda, salt, ginger, cinnamon, nutmeg, and cloves in a bowl.
Cream softened butter with brown sugar until fluffy, 2 to 3 minutes.
Beat in molasses and vanilla until smooth and glossy.
Add eggs one at a time, mixing well after each. Scrape the bowl.
Blend in sour cream until fully combined.
Add dry ingredients in three additions, alternating with milk, beginning and ending with dry. Mix just to combine.
Divide batter evenly among liners, filling about two-thirds full.
Bake 18 to 20 minutes, until a toothpick comes out clean. Cool completely on a rack.
Make frosting: Beat cream cheese and butter until creamy. Gradually add powdered sugar, cinnamon, vanilla, and salt.
Drizzle in cream to reach a smooth, spreadable texture. Beat 30 seconds to lighten.
Swirl frosting onto cooled cupcakes. Dust with a pinch of cinnamon if you like.