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 (cut side down) and saute over medium-high heat until the mushrooms and Brussels sprouts begin to caramelize (about 6 minutes). Turn and saute 6 more minutes. Add the 2 tablespoons of pomegranate balsamic to the pan stirring and scraping to deglaze, about 2 minutes. 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.