Make the crust:
Position a rack in the center of the oven and heat the oven to 350°F.
Pulse the cookies in a food processor until very finely ground. With the processor running, pour the melted butter through the feed tube and process until combined. Transfer the mixture to a 9-inch glass pie plate and press it firmly into the bottom and up the sides. Bake until the crust is firm in the center and fragrant, 10 to 12 minutes. Transfer to a wire rack to cool completely.
Make the filling:
Fill a 3-quart saucepan with about 1 inch of water and bring to a simmer over medium-low heat. Put the chocolate liqueur in a small bowl. Sprinkle the gelatin over the top and let stand at least 5 minutes.
Meanwhile, put the chocolate in a medium bowl. Separate the eggs, putting the whites in another medium bowl and the yolks in a large metal bowl.
Whisk 1/4 cup of the sugar into the yolks until combined, then whisk in the milk and the salt. Set the bowl over the pot of simmering water (the bottom of the bowl should not touch the water) and cook, stirring constantly with a wooden spoon, until the mixture coats the back of the spoon and holds a line when you draw your finger through it, 4 to 6 minutes. (The custard should reach at least 160°F on an instant-read thermometer and should not go over 180°F.) Remove from the heat.
Whisk the gelatin mixture into the hot custard until completely melted. Pour the custard over the chocolate and let stand 1 minute. Whisk until the chocolate is melted, then whisk in the heavy cream and vanilla.
Prepare an ice water bath by filling a large metal bowl with a few inches of ice and water. Put the bowl of chocolate custard in the ice water bath and whisk constantly until the mixture is just thick enough to hold a ribbon when drizzled over itself, about 3 minutes. Immediately remove from the ice water bath.
Beat the egg whites with an electric mixer on medium speed until soft peaks form, 2 to 3 minutes. Beat in the remaining 1/4 cup of sugar, 1 Tbs. at a time, and continue to beat just until stiff peaks form, 1 to 2 minutes more.
Gently whisk a third of the egg whites into the cooled chocolate custard to lighten it. Fold in the remaining whites. Spoon the mixture into the chocolate crust and refrigerate until firm, at least 4 hours.
Make the topping:
Put the cream and sugar in a chilled medium bowl and beat with an electric mixer on medium-high speed until soft peaks form, about 2 minutes. Spoon the whipped cream on the pie.
If you like, decorate the pie with chocolate shavings by slightly heating the chunk of chocolate (30 to 50 seconds in the microwave, or pass a side briefly over a flame) and shaving it with a vegetable peeler onto the pie. Serve chilled.
The pie can be made and filled up to 24 hours ahead and refrigerated. The pie can be topped up to 1 hour ahead; refrigerate until ready to serve.