Preheat oven to 350 degrees Fahrenheit and line cookie sheets with nonstick liners or spray lightly with nonstick cooking spray.
In the bowl of an electric mixer, cream together softened butter, brown sugar, granulated sugar, eggs, and vanilla.
In a separate bowl, whisk together flour, baking cocoa, baking soda and salt.
Add flour mixture to wet mixture and mix just until incorporated. Mix in 3/4 c. Thin Mints cookie crumbs.
Form dough into 1 1/2" balls and place on prepared cookie sheet at least 2" apart.
Flatten dough balls with palms of hands.
Place cookies in the oven and bake for approximately 7-8 minutes. No more than 8 minutes.
Remove from the oven and let them sit for a few minutes, then carefully remove them to a cooling rack to cool completely.
To make the frosting, cream together softened butter, powdered sugar, mint extract, green food coloring, and milk. Add the milk slowly, one Tablespoons at a time, creaming in between, just until a nice creamy consistency is reached. Gently fold in 1/2 c. Thin Mints cookie crumbles. Frost sandwich cookies.