In a large heatproof bowl, combine the milk and bittersweet chocolates.

In a medium saucepan, bring the milk, heavy cream, and sugar to a boil, whisking constantly until the sugar is dissolved. In a medium heatproof bowl, whisk the egg yolks. Gradually whisk in half of the hot cream. Whisk the egg-and-cream mixture into the saucepan and cook over moderate heat, stirring with a wooden spoon, until the custard coats the back of the spoon, about 4 minutes. Pour the custard over the chocolate and let stand for 2 minutes, then stir until smooth.

Transfer the mixture to a blender and puree until very smooth, about 1 minute. Pour the mixture into eight 4-ounce ramekins and refrigerate until chilled, 2 hours.

Let the pots de creme stand at room temperature for 15 minutes. Garnish with creme fraiche and chocolate shavings; serve.

The pots de creme can be refrigerated for up to 3 days.