Using a hand mixer, blend together the whole milk, brown sugar and granulated sugar until sugars are dissolved.
Slowly add the cocoa powder and blend well.
Add the heavy cream and mix until blended and smooth.
Add the mixture to an ice cream maker.
Note: Manufacturers may be different, but in a Cuisinart Pure Indulgence, churn for 15 minutes.
Add the chocolate chips and marshmallows and churn for about another 15 minutes.
Put the churned ice cream into a 2 qt container and freeze overnight to firm.
Serve and enjoy!