Preheat the oven to 325 degrees F. Wrap the bottom of a 9-inch springform pan with foil. Grease the springform pan and set aside.
In a small bowl, combine the graham cracker crumbs, brown sugar, vanilla extract, and melted butter. Press the crust into the bottom of the springform pan and halfway up the sides. Sprinkle the mini chocolate chips and mini marshmallows across the bottom of the crust. Set aside.
In the bowl of a stand mixer, beat the cream cheese on medium speed until fluffy and smooth. Scrape the bottom and sides of the mixing bowl. Beat again for another minute or two.
Add the corn starch and granulated sugar. Mix until combined.
Add the sour cream, heavy cream, and vanilla extract, beating until everything is well mixed. Make sure to scrape down the sides and bottom of the bowl at least once.
To avoid having the top of the cheesecake crack during baking, set the springform pan inside of an oven safe baking pan that is larger than your springform pan. Add water to the baking pan so that it comes halfway up the sides of the springform pan.
Take the cheesecake out of the oven and out of the water bath, and set it on a wire rack. Wait 10 more minutes.
Run a butter knife between the cheesecake and springform pan to carefully separate it. Let it cool for another hour.
Spread warmed fudge sauce over the top of the cheesecake. Top with mini marshmallows in an even layer so that the entire top is covered.
Put the cheesecake under the broiler for about 30 seconds or until the marshmallows are toasted.
Let the cheesecake cool completely. Cover and refrigerate for at least 4 hours. Slice and serve!