Preheat oven to 350°F. Bake the chocolate cake mix according to package directions in a greased 9x13 inch pan. Let cool for 10 minutes.
Using the handle of a wooden spoon, poke holes all over the warm cake, spacing them about 1 inch apart and going about 2/3 of the way down.
In a microwave-safe bowl, combine sweetened condensed milk, 12 oz chocolate chips, and 1/3 cup heavy cream. Microwave in 30-second intervals, stirring until smooth and pourable.
Pour the chocolate mixture evenly over the cake, making sure it runs into all the holes. Refrigerate for at least 1 hour until the filling sets.
For the topping, whip 1 1/2 cups heavy cream with powdered sugar and vanilla until stiff peaks form. Gently fold in the marshmallow fluff by hand with a wooden spoon.
Spread the marshmallow whipped cream evenly over the cooled cake.
Melt 1/2 cup chocolate chips with 3 tablespoons heavy cream until smooth. Transfer to a zip-top bag, snip the corner, and pipe lines across the cake. Drag a toothpick through the lines to create swirls.
Refrigerate for at least 30 minutes before serving. Store covered in the refrigerator for up to 5 days.