Preheat oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.
Prepare the cake mix according to the package instructions. Pour the batter evenly into the prepared pans and bake for 30–35 minutes or until a toothpick inserted comes out clean.
While the cake is baking, prepare the filling: In a bowl, combine marshmallow creme, powdered sugar, and vanilla extract. Mix until smooth and set aside.
Once the cakes are done, let them cool in the pans for 10 minutes before removing them to a wire rack to cool completely.
Once the cakes are cool, slice them in half horizontally to create four layers.
Spread the marshmallow filling between the cake layers.
For the glaze: In a saucepan, heat heavy cream and butter over medium heat until the butter is melted. Remove from heat and stir in the chocolate chips until smooth.
Pour the chocolate glaze over the assembled cake and let it set for 30 minutes before serving.