Preheat the oven to 400°F (200°C). Generously butter a 9-inch pie dish and set it aside.
Make the choux-style pie shell: in a medium saucepan over medium-high heat bring 1/2 cup water, 1/4 cup butter, and 1/8 teaspoon salt to a boil.
Once boiling, reduce heat to low and add 1/2 cup all-purpose flour. Stir constantly until the mixture forms a ball and pulls away from the sides of the pan.
Remove from heat and, while stirring, add the 2 large eggs one at a time, mixing well after each addition until fully incorporated and smooth.
Using buttered hands or a spatula, press the dough into an even layer on the bottom and up halfway on the sides of the prepared pie dish.
Bake the pie shell in the preheated oven for 35 minutes, until golden brown. Remove and cool completely in the pie dish.
While the shell bakes, make the chocolate sauce: combine 1/2 cup semi-sweet chocolate chips and 1/2 cup heavy cream in a microwave-safe bowl. Microwave at 50% power in 30-second intervals, stirring between intervals, until smooth and melted. Cool completely.
Prepare the pastry cream: in a large bowl whisk together 1 cup heavy cream, 1 cup milk, and the 5.1 oz package instant pudding mix for about 3 minutes until thickened.
Spread the pastry cream evenly into the cooled puff pastry pie shell, smoothing the top with a spatula.
Whip the topping: in a clean bowl beat 3/4 cup heavy cream with 3 tablespoons granulated sugar using an electric hand mixer until stiff peaks form.
Spread the sweetened whipped cream evenly over the pastry cream layer.
Cut the pie into slices and drizzle each slice with the cooled chocolate sauce. Serve immediately.