Preheat oven to 350℉. Line a cupcake pan with cupcake liners. In a small bowl, whisk together the flour, baking soda and salt and set aside.
In the bowl of a stand mixer, cream together the butter, brown sugar and white sugar on medium. When it is well blended, beat in the vanilla extract. Then add the eggs, one at a time until combined. Add half of the flour mixture. When that is mixed in, set the mixer to low and add the milk. When that is mixed in, return the mixer to medium and add the rest of the flour mixture until just combined.
Using a spatula, stir the chocolate chips and marshmallows into the batter until spread out. Place the batter into the prepared pan and put in the oven for 15-17 minutes. Remove from oven and let cool on a wire rack before frosting.
Frosting
In a medium saucepan, combine the butter, milk and sugar. Bring to a boil. Then remove from heat and add the chocolate chips and vanilla extract. Beat until cool and frost immediately.