Start by crushing the chocolate sandwich cookies into fine crumbs.
Combine the crushed cookies with melted butter and press firmly into the bottom of a 9x13 inch pan.
In a mixing bowl, beat the softened cream cheese, granulated sugar, and vanilla extract until smooth and creamy.
Fold in 1 1/2 cups of whipped topping gently into the cream cheese mixture.
Spread the cream cheese layer evenly over the chilled cookie crust.
Prepare the instant chocolate pudding by whisking it with 1 1/2 cups cold milk until thickened, about 2 minutes.
Spread the chocolate pudding layer over the cream cheese layer in the pan.
Prepare the instant vanilla pudding similarly with 1 1/2 cups cold milk and whisk until thickened.
Once thickened, spread the vanilla pudding layer over the chocolate pudding layer evenly.
Spread the remaining 1 1/2 cups of whipped topping on the top layer.
Chill the completed cookie lasagna for at least 4 hours, or overnight if possible, before serving.