In a large saucepan, combine sugar, milk, vanilla, and butter.
Bring to a boil over medium high heat, stirring constantly. Once boiling, keep at a rolling boil for a full two minutes (still stirring).
For this next step, I use a stand mixer with whisk attachment (a hand mixer would work too). Combine the marshmallow cream and milk chocolate chips in mixing bowl. Pour hot mixture over these ingredients and blend until smooth. I turn my mixer on medium speed and blend for 1-3 minutes, scraping down sides of bowl as needed.
While this is mixing, line an 8-inch square baking dish with parchment paper. Crumble half of the frozen cookie dough (in small 1inch chunks) into bottom of baking dish. Set aside.
Once mixture is smooth, pour into prepared dish. With the remaining cookie dough, press small chunks into the top of the fudge. Refrigerate for 4 hours, or overnight. Cut and enjoy.
Store fudge in airtight container for up to 1 week.
Notes
Use a stand mixer: An electric mixer makes life easier when you're making fudge! You'll pour the hot butter and milk mixture right over the marshmallow cream and chocolate chips, then let the mixer do its thing.
Freeze the cookie dough first: As the fudge sets the cookie dough will thaw to the perfect consistency and temperature.
Food safety: If you're making your own cookie dough, you will need to heat treat (bake) the flour you use first. See our guide for how to heat treat flour.
Flavor variations: Once you know how to make cookie dough fudge, you can swap out the chocolate for any flavor you like. Chocolate Peanut Butter Fudge would be delicious!