Fill a large bowl with ice. The bowl should be large enough to hold a medium saucepan.
In a medium saucepan over low heat, combine marshmallows, milk, and chocolate. Whisk constantly until melted and smooth, about 5 minutes.
Set the saucepan inside the large bowl with ice. Let stand, whisking occasionally, until the chocolate mixture has cooled and thickened, about 20 minutes.
In a standing mixer with the whisk attachment, or using an electric hand mixer, whip cream and vanilla together until soft peaks form, about 3 minutes.
Fold whipped cream into the chilled chocolate mixture (do not overmix). Spoon into wine glasses or ramekins and cover with plastic wrap (the plastic should be directly on the surface of the mousse). Refrigerate at least 6 hours or overnight.
Garnish with whipped cream and chocolate shavings before serving if desired.