Preheat oven to 375-degees F. Oil a baking pan well; set aside.
Remove any damaged or discolored outer leaves from Brussels sprouts. Trim stem-end. Cut brussels sprouts in half lengthwise.
In a medium-sized bowl, put sprouts and coat well with extra virgin olive oil. Toss sprouts to coat well.
Sprinkle with salt and a little pepper, then toss to distribute well.
Pour some balsamic vinegar over the brussels sprouts and toss. The balsamic will not stick well to the brussels sprouts because of the olive oil. Not to worry, more balsamic can be added following roasting.
Place brussels sprouts, cut side down, on the well oiled baking pan. Roast in oven for 15 minutes.
Remove the pan from the oven and turn each sprout over so that the cut side is facing up. Return pan to oven and roast the sprouts for an additional 10-15 minutes, until lightly caramelized on the surface.
Serve with extra balsamic vinegar, to taste.