Heat a heavy-duty 12" saute pan, add the olive oil. Add the shallot and saute over medium until translucent. Add the mushrooms and Brussels sprouts and saute over medium-high heat until the mushrooms and Brussels sprouts begin to caramelize (about 6 minutes). Add the 2 tablespoons of pomegranate balsamic to the pan stirring and scraping to deglaze. (Make sure to scrape up the browned bits of mushroom and shallot at the bottom while evenly coating the Brussels sprouts). Season with salt and pepper to taste. Serve immediately.