Preheat the oven to 325 degrees F (165 degrees C). Grease two 12-cup muffin tins or line cups with paper liners.

Whisk flour, cocoa powder, baking soda, baking powder, espresso powder, cinnamon, and salt together in a bowl. Whisk in white sugar and brown sugar.

Beat eggs, water, and vanilla extract together in a separate bowl. Add sour cream and oil and beat well. Add egg mixture to the bowl with the flour mixture and mix well until no dry spots remain. Spoon batter into the prepared muffin cups, filling each 3/4 full.

Bake in the preheated oven until tops spring back when lightly pressed, 18 to 20 minutes. Cool in the tins for 5 minutes. Transfer to a wire rack to cool completely, about 20 minutes.

Meanwhile, place cream cheese and butter into the bowl of a stand mixer and cream together until smooth. Add vanilla extract and mix. Add confectioners' sugar and mix on medium-low speed; whip into a firm consistency, 2 to 5 minutes. Frosting will thicken as you whip. Add milk 1 tablespoon at a time to thin if necessary.

Crush whole cookies into crumbs in a food processor. Mix cookie crumbs into frosting using a rubber spatula. Chill frosting in the refrigerator for about 15 minutes before piping onto cooled cupcakes.