Preheat the oven to 350°F.
In a large bowl, use two knives or a pastry cutter to cut 2 cups all-purpose flour and 1 cup (2 sticks) room-temperature butter together until the mixture is crumbly and resembles coarse crumbs. Press the mixture evenly into the bottom of a 9×13-inch pan.
Bake the crust about 25 minutes, until golden. Remove from the oven and allow the crust to cool completely.
In a medium bowl, use an electric mixer to beat the two 8-ounce packages cream cheese and 1 cup granulated sugar until smooth and lump-free. Spread this cream cheese mixture evenly over the cooled crust.
In a separate medium bowl, whisk together 3½ cups milk and the two 3.4-ounce boxes instant lemon pudding mix until the pudding is fully thickened (about 2 minutes). Spread the pudding evenly over the cream cheese layer.
Refrigerate until the pudding layer is set, at least 30 minutes.
Spread 12 ounces of Cool Whip evenly over the chilled pudding layer. Slice and serve.