For the cupcakes: Preheat the oven to 350 degrees and line 12 muffin cups with paper or aluminum foil liners.
In a medium bowl or on a large square of waxed paper, sift together the flour, cocoa powder, baking soda, baking powder and salt and set aside.
In a large bowl, whisk together the milk and vinegar; set aside for a few minutes to curdle.
Add the sugar, oil and vanilla extract and other extract, if using, and beat until foamy. Add the dry ingredients in 2 increments, and beat until no large lumps remain.
Add the chopped cookies to the batter, stirring just to combine. Spoon the batter into the liner cups, filling them three-quarters full.
Bake for 18 to 20 minutes or until a toothpick inserted into the center comes out clean.
Transfer to a wire rack to cool completely.
Frosting:
While cupcakes cook, in the bowl , beat the shortening and butter on medium-high speed for about 5 minutes, until well combined and fluffy.
Reduce speed to low to add the sugar until incorporated, and then increase to medium-high speed to beat for about 3 minutes.
Add the vanilla extract and milk; beat on the same speed for 5 to 7 minutes, until fluffy. Add the cookie crumbs, mixing well.