Heat a large skillet over medium-high heat, and add the olive oil. Add the shallots and sauté for 3 minutes until tender.
Add the slivered Brussels sprouts, season with salt and pepper, and sauté for 5 to 10 minutes, until the Brussels sprouts are wilted or as soft as you would like them. Stir in the balsamic vinegar and let it simmer and coat the Brussels sprouts.
Serve hot or warm, with the bacon and/or Parmesan, if desired.
Notes
Cooking down the vinegar in the pan brings out its natural sweetness and thickens it into a glaze for the Brussels sprouts.
You can buy shredded Brussels sprouts if you're short on time.
True balsamic vinegar (known as aceto balsamico in Italian) is made only in Modena, Italy, and has been aged for a minimum of 12 years, up to 25, in a strictly delineated process. It is made from grape must (musto), which are essentially crushed grapes, with the skin and seeds and everything included. It is dark and fairly thick and has a notable level of sweetness playing into the tanginess. This is pretty pricy stuff, but if you love it and want to splurge, here is a great place to use it.