In a large bowl, mix the instant chocolate pudding mix with cold milk according to the package instructions.
In a separate bowl, beat the softened cream cheese until smooth.
Gradually add the softened butter, powdered sugar, and vanilla extract to the cream cheese, mixing until light and fluffy.
Gently fold half of the whipped cream cheese mixture into the pudding to blend.
In another bowl, crush the chocolate sandwich cookies into coarse crumbs.
In a 9-inch springform pan or a rectangular dish, spread half of the crushed cookie crumbs evenly onto the bottom.
Pour the pudding and cream cheese mixture over the cookie layer.
Sprinkle the remaining half of the crushed cookies on top for a “dirt” effect.
Gently press a few gummy worms into the top to resemble wriggling through the cake.
Chill the dessert for at least 2 hours before serving.