To a small pan or pot add 1/4 c milk and the instant coffee granules. Heat just until the coffee dissolves. Remove from the heat so it can can cool.
To a mixing bowl add both boxes of the pudding mix and 3 c milk. Whisk well and set aside to thicken.
To a food processor add 2 sleeves of Oreos from a family size pack. Process. Add a stick of melted butter to the food processor and pulse until combined. Add the buttery crumb miture to a 9x13 pan and press flat with the bottom of a glass. Place in the refrigerator.
To a separate bowl or stand mixer add softened cream cheese, powdered sugar and vanilla. Beat until smooth. Fold in 1 cup of the thawed Cool Whip. Set aside.
By now the coffee milk mixture is ready to be whisked into the pudding (which should be very thick). Whisk until combined.
Add the remaining sleeve of Oreos to a gallon size ziploc bag and smash with a rolling pin to create large crumbs.
Add 1 cup of the Oreo crumbs to the pudding. Mix until well combined.
To assemble, evenly spread the cream cheese layer on top of the Oreo crust followed by all of the pudding mixture. Top with the remaining Cool Whip and Oreo crumbs.
Refrigerate for 4+ hours. Serve chilled.