Preheat the grill or oven to 350°.
If using a grill, set it up for indirect heat.
Lightly grease a 9x9 baking dish or a 12-inch skillet.
Remove the cinnamon rolls from the tube, setting the icing aside.
Cut each roll into quarters and arrange them evenly in the prepared dish.
Sprinkle the blueberries over the top.
In a small bowl, whisk together the melted butter and brown sugar until well combined.
Pour the mixture evenly over the cinnamon rolls, then follow with the heavy cream.
Bake for 25-30 minutes, or until golden brown and bubbly.
Let cool for about 5 minutes, then spread the icing evenly over the top.
Serve warm.