Mix the 1 1/2 cups of crushed Oreos with the melted butter. Press this mixture firmly into the bottom of a 9-inch springform pan. Chill the crust for 15 minutes.
In a large bowl, beat the softened cream cheese until smooth.
Gradually beat in the powdered sugar until fully combined.
Mix in the vanilla extract and milk until the mixture is creamy.
Gently fold in the thawed whipped topping until no streaks remain. Do not overmix.
Spread the cream cheese mixture evenly over the chilled crust.
Cover the cheesecake loosely with plastic wrap and refrigerate for at least 6 hours, or preferably overnight, until firm.
Before serving, sprinkle the remaining 1 cup of crushed Oreos over the top. Release the springform side carefully.
Notes
For a firmer crust, bake the butter and cookie mixture at 350°F for 8 minutes, then cool completely before adding filling.
Use full-fat cream cheese for the best creamy texture.
If you prefer individual servings, press the crust into the bottom of cupcake liners or small glasses and chill for 4 hours.