Heat the oven to 325°F/160°C.
Put the chocolate in a bowl. Bring the cream, milk, and sugar to a boil in a saucepan. Remove from the heat and add the shredded chocolate, stirring to melt. (Be sure to give it enough time: you don’t want little bits floating around in there.) Gradually whisk over the egg and strain the mixture into the baked tart shell. Bake until set, about 20 minutes. Cool completely.