Preheat oven to 350 degrees. Line a muffin tin with cupcake liners.
In a large mixing bowl, combine the butter or oil, flax eggs, sugar and vanilla. Beat with a hand mixer until smooth.
Add in the applesauce, vinegar, non-dairy milk, salt. Beat again. Then add in the cocoa powder and flour. Beat until a fluffy and smooth batter forms.
Fill the cupcake tins and bake at 350 for 18-22 minutes or until a toothpick comes out clean when inserted into the center of the cupcake.
Cool cupcakes for at least an hour before adding frosting.
Frosting: Using a mixer, whip together the sugar and non-dairy milk. Add non-dairy milk as needed to thin out the frosting a bit. Finish off by hand folding in the crushed cookies.
When cupcakes are cooled, you can swirl the frosting on top. I used a spoon to add the frosting since having cookies in the frosting makes it chunky and therefore not a good candidate for a pastry bag swirl. Finish with a cookie or half cookie on top of the frosting. Serve! Chill in the fridge until ready to eat.