Preheat oven to 350°F.
Keep the rolls together as a slab and transfer to a baking tray lined with parchment paper. With a sharp knife, cut into each roll in a swirl pattern about 3/4 of the way down, starting from the outside moving towards the center, without slicing all the way through.
In a bowl, whisk together the melted butter, brown sugar, and cinnamon until it resembles lava. Pour the mixture all over the rolls, letting it seep into the cuts. Allow the rolls to soak for 10 to 15 minutes.
Bake for 10 minutes, until golden on top and gooey inside.
While baking, beat cream cheese and butter until smooth. Add powdered sugar, vanilla, and heavy cream, mixing until fluffy.
Spread the frosting over the warm rolls or serve on the side for dipping.