Whisk together milk, cream, and 1/2 cup white buttermints in a medium saucepan. Bring to a simmer over medium, stirring constantly, until mints are dissolved and mixture is hot, about 13 minutes. Remove from heat and whisk in chopped white chocolate and vanilla until smooth. Stir in Irish cream liqueur. Pour into 4 serving cups, and top each with 1/4 cup marshmallows. Garnish, if desired.