Unroll pie crust and shape to fit a 9-inch pie pan, using your fingers to crimp the edges. Prick bottom all over with a fork. Bake pie crust for 9 to 11 minutes. Let cool.
In a small pan set over low heat, melt 3/4 cup chocolate chips with 1 1/2 tablespoons butter, and 1 tablespoon water. Whisk continuously until smooth. Whisk in powdered sugar. If too thick, add a little more water. Spread evenly on bottom of pie shell. Refrigerate.
To make peanut butter filling, combine butter and brown sugar in a medium saucepan. Cook over medium heat, stirring frequently, until butter is completely melted. Place in refrigerator for 10 minutes.
Transfer brown sugar mixture to a large bowl and beat it together with the peanut butter using an electric mixer. Add whipped topping and beat on low speed just until mixed in. Pour over chocolate layer and return pie to refrigerator.
Make topping. In a small saucepan over low heat, melt chocolate chips with butter, milk, and corn syrup. Stir continuously until smooth. Spread evenly over filling. Refrigerate until ready to serve.