Bake cinnamon rolls per directions on the back of the container. Save the icing for later. Let the cinnamon rolls sit out over night.
Preheat oven to 350 degrees. Mix together the eggs, 2 cups eggnog, brown sugar, cinnamon and vanilla in a large bowl. Cube cinnamon rolls and place in prepared 8-inch baking dish. Pour melted butter on top of the rolls, add the custard and press down so they are covered in liquid. Let sit 30 minutes. Bake for 35 minutes, cover with foil and bake 10 additional minutes.
While the bread pudding is cooking, make the icing by mixing together the packaged icing, powdered sugar and remaining eggnog.