Make the crust: Preheat the oven to 350 degrees F. Pulse the cookies, granulated sugar and salt in a food processor until finely ground. Add the melted butter and pulse until the mixture starts to clump. Transfer to a 9-inch fluted tart pan with a removable bottom and firmly press on the bottom and up the side of the pan. Bake until the crust is firm, 12 to 15 minutes. While the crust is still warm, use the back of a spoon to gently press any cracks together. Transfer to a rack to cool completely.
Make the filling: Heat 1 cup milk in a medium saucepan until hot but not boiling. Meanwhile, whisk the egg yolks, granulated sugar, cornstarch, 1 tablespoon cocoa powder, the vanilla, salt and the remaining 1/2 cup milk in a large bowl. Gradually whisk the hot milk into the egg yolk mixture until smooth. Pour the mixture into the saucepan and cook, whisking constantly, until it comes to a boil and is thick like pudding, 3 to 5 minutes. Remove from the heat and whisk in the chocolate until melted. Pour the filling into the crust and smooth the surface with an offset spatula. Gently press plastic wrap directly onto the surface to prevent a skin from forming. Refrigerate until cold and set, about 2 hours.
Make the topping: Beat the heavy cream, confectioners' sugar and remaining 3 tablespoons cocoa powder in a large bowl with a mixer on medium speed until soft peaks form. Spread the cocoa whipped cream on the tart and top with sprinkles.