Preheat the oven to 340°F (170°C). Line two standard muffin pans with 20 paper liners.
Crush cookies: Pulse enough cookies to make 1 3/4 cups small chunks for the batter and 3/4 cup very fine crumbs for the frosting. Spread the fine crumbs on a small tray and let them air-dry while you begin the frosting (this helps keep the frosting from loosening).
Make the frosting first: In a stand mixer fitted with the paddle, beat butter on medium speed until creamy and slightly lighter, about 2 minutes. In a small cup, stir together the heavy cream, vanilla, molasses, and espresso powder until the espresso dissolves.
Add half the powdered sugar to the butter and mix on low until incorporated. Stream in half of the cream mixture; beat on medium-high for 30 seconds. Add the remaining powdered sugar followed by the rest of the cream mixture; beat 1–2 minutes until fluffy. Fold in the cooled fine cookie crumbs by hand. Cover and refrigerate 10–15 minutes to set while you make the cupcakes.
Whisk dry ingredients: In a medium bowl, whisk together flour, baking powder, salt, and cinnamon until evenly combined.
Build the batter: In a large bowl, whisk sugar and eggs vigorously for 45–60 seconds until slightly thick and pale. Slowly whisk in the oil. Add sour cream and vanilla and whisk until smooth.
Alternate dry and wet: Using a spatula, fold in half of the dry mixture, then half of the milk. Repeat with the remaining dry mixture and milk, starting and ending with dry. Stop folding when a few small streaks of flour remain, then gently fold in the 1 3/4 cups chopped cookie pieces. Rest the batter 5–8 minutes to hydrate for a softer crumb.
Portion and bake: Divide batter among liners, filling each about 2/3 full. Tap the pans gently on the counter to release air pockets. Bake 17–20 minutes, rotating the pans halfway, until the tops spring back and a toothpick comes out clean or with a few moist crumbs.
Cool and finish: Cool cupcakes in the pan 5 minutes, then transfer to a wire rack and cool completely. Re-whip the chilled frosting for 10–15 seconds to refresh. Pipe tall swirls onto each cupcake and top with a mini chocolate chip cookie, if using.