Prepare the crust: Mix the chocolate cookie crumbs and melted butter until combined. Press the mixture evenly into the bottom and up the sides of a 9-inch pie plate. Chill the crust for at least 30 minutes.
Make the chocolate base: In a medium saucepan, combine the sweetened condensed milk and chocolate chips. Heat over medium-low heat, stirring constantly until the chocolate chips are fully melted and the mixture is smooth. Remove from heat and stir in 1 teaspoon vanilla extract. Pour this mixture into the chilled crust. Set aside.
Prepare the pudding: In a large bowl, whisk together the instant chocolate pudding mix and 2 cups cold milk until the mixture thickens, about 2 minutes. Gently fold the warm chocolate base mixture from step 2 into the thickened pudding until just combined. Spread this filling evenly over the crust.
Chill the pie: Cover the pie loosely with plastic wrap and refrigerate for at least 4 hours, or preferably overnight, until the filling is firm.
Make the whipped cream topping: In a separate bowl, beat the heavy whipping cream, powdered sugar, and 1 teaspoon vanilla extract with an electric mixer until stiff peaks form.
Top and decorate: Spread or pipe the whipped cream over the chilled chocolate filling. Garnish with chocolate curls or holiday sprinkles before serving. Keep refrigerated until ready to serve.
Notes
You can prepare the entire pie, including the whipped cream topping, up to 24 hours in advance. Keep it covered in the refrigerator.
For a festive look, use red and green holiday sprinkles on top of the whipped cream.
If you do not have strong brewed coffee, use hot water instead; the coffee deepens the chocolate flavor.