In a small saucepan, whisk the milk, cream, chocolate syrup, and vanilla extract over medium-high heat and simmer for about 3 minutes.
Once heated, whisk in green food coloring until combined into a Grinch-like green color.
Now it’s time to decorate the rim of the mug. Pour some peppermint sugar sprinkles into a shallow bowl. Wet the mug's rim with water and gently press it into the sprinkles until the edge is coated.
Pour the hot chocolate into the mug and top with marshmallows and sprinkles.
Notes
Don’t overheat: Simmer gently to avoid burning the chocolate syrup. Mix evenly: Add food coloring slowly and whisk until smooth. Rim last: Coat mug rims right before pouring so sprinkles stick. Serve warm: Enjoy straight from the stovetop while it’s hot and creamy.