Place the cinnamon rolls in the baking dish, leaving a little space between them.
Pour the eggnog over top of the cinnamon rolls and around the bottom of the pan.
Melt 3 tablespoons of butter in the microwave. Add in the brown sugar and cinnamon and mix well. Pour over top of the cinnamon rolls.
Cover the top of the pan with foil and bake for 25-30 minutes. Remove from oven, remove foil, and let cool 5 minutes.
Meanwhile, place the icing from the cinnamon rolls in a bowl. Add in the remaining butter, remaining eggnog, cream cheese, and vanilla. Beat with a mixer until smooth.