Using a vegetable peeler, shave chocolate into curls; set aside.
Place white chocolate in a medium heat-proof bowl; set aside. Place milk and cream in a medium saucepan set over medium heat until bubbles begin to form around edges of pan (about 4 minutes). Do not boil.
Remove mixture from the flame. Immediately pour over white chocolate. When chocolate begins to melt, gently stir to combine.
Whisk in vanilla. Continue whisking until light foam forms.
Serve immediately. Garnish with chocolate shavings or Martha's Homemade Marshmallows