Preheat oven to 400°F with the oven rack in the center position.
In a large cast iron skillet or another oven-safe skillet, heat olive oil over medium-high heat. Add Brussels sprouts to skillet, seasoning with salt and pepper to taste.
Stirring occasionally, cook Brussels sprouts until they begin to brown (a few minutes).
Once browned, transfer skillet into the preheated oven. Roast for 15-20 minutes, making sure to stir halfway through. Brussels sprouts are ready to be removed when they turn a rich brown color and are tender.
While the Brussels sprouts are in the oven, combine maple syrup and balsamic vinegar in a small skillet over medium-high heat. Bring the mixture to a boil and stir constantly, and then reduce the heat to medium. Continue the stirring process until the mixture has reduced to about ⅓ of its original volume. It will be syrupy and thick. (Be careful not to overcook; it will become sticky.)
Transfer baked Brussels sprouts to a plate and drizzle with maple-balsamic reduction. Season to taste with salt and pepper.