Preheat oven to 350°F. Line a 12-cup muffin pan with paper liners.
Crush cookies. Keep coarse pieces for batter and fine crumbs for frosting and topping.
Whisk flour, sugar, baking powder, baking soda, and salt in a large bowl.
Whisk milk, sour cream, oil, and vanilla in a separate bowl until smooth.
Pour wet ingredients into dry. Stir gently just until no dry streaks remain.
Fold in the coarse cookie pieces. Do not overmix.
Divide batter among liners, filling each about two-thirds full.
Bake 17 to 20 minutes, until a toothpick comes out clean. Cool 10 minutes, then move to a rack.
Beat softened butter until light and fluffy, about 2 minutes.
Gradually mix in powdered sugar and the salt. Beat until thick and smooth.
Stream in heavy cream and vanilla. Beat until creamy and spreadable.
Blend in the fine cookie crumbs. If needed, add a splash of cream to loosen.
Swirl frosting onto completely cooled cupcakes. Sprinkle with chopped cookie pieces.