Preheat over to 425 degrees Fahrenheit

Toss brussels sprouts with 3 Tbsp olive oil, salt, and pepper. Spread on a baking sheet and bake for 25 to 30 mins or until tender.

While the brussels sprouts are cooking heat the remaining oil in a wide sauteeing pan over medium heat.

Add the shallots and stir occasionally. Depending on the temperature of your stove, you may need to turn down the heat if they begin to burn. After about 10 mins add a pinch of salt. Continue to cook until the onions are a rich brown color (about 30 mins).

Add the vinegar to the pan and cook until reduced by about half. Pour over the brussels sprouts and mix together.