Preparation

Make the filling:

• Melt together the chocolate, milk, and butter in a medium bowl in a microwave or in a double boiler over medium heat (seeHow to melt chocolate). Add the vanilla and salt. Whisk the mixture until well blended and smooth. Set aside, whisking occasionally, until room temperature and slightly thickened, about 1 hour. (For faster cooling, refrigerate the filling until thickened to a pudding consistency, about 30 minutes, whisking and scraping the sides of the bowl with a rubber spatula every 5 minutes.)
• With a rubber spatula, scrape the mixture into the crust and spread evenly, taking care not to disturb the edge of the crust. Let cool completely, cover, and refrigerate until the filling is set, about 4 hours and up to 8 hours before proceeding with the recipe.

Make the topping:

• In a medium bowl, combine the mascarpone, cream, sugar, and vanilla. Using an electric mixer, beat on low speed until almost smooth, 30 to 60 seconds. Increase the speed to medium high and beat until the mixture is thick and holds firm peaks, another 30 to 60 seconds. Don’t overbeat.
• With a rubber or metal spatula, spread the topping over the chocolate filling, leaving lots of swirls and peaks. Serve the tart right away or cover loosely and refrigerate, in the pan, for up to 4 hours.