Preheat your oven to 350°F (175°C).
In a large bowl, cream together butter, sugars, eggs, and vanilla.
In another bowl, mix flour, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients.
Stir in marshmallows and chocolate chips.
Drop spoonfuls of dough onto a baking sheet.
Bake for 10-12 minutes, until golden brown.
While the cookies bake, heat milk, cream, cocoa powder, sugar, and chocolate chips in a pot or microwave.
Whisk until smooth, then add vanilla extract.
Serve the cookies warm with your hot chocolate.