Finely crush chocolate cookies in a food processor; set crumbs aside.
Combine cream cheese, butter, and confectioner's sugar in a large bowl; beat with an electric mixer until smooth.
Whisk milk, whipped topping, and pudding together in a separate large bowl; fold in cream cheese mixture until well combined.
Alternately layer crushed cookies and pudding mixture in a medium flower pot, starting and ending with cookies. Chill dirt cake in the refrigerator until ready to serve; garnish as desired.