Preheat the oven to 400°, making sure the oven rack is in the center position
In your oven-safe skillet, (I prefer cast iron), heat the olive oil over medium-high heat.
When the oil is hot (test by spritzing a little water and looking for a sizzle), add the brussels sprouts and season with salt and pepper. Stirring occasionally until the sprouts get a light brown coloring.
Transfer the skillet into the preheated oven and roast for 15-20 minutes. Halfway through, stir them around. When they have a rich brown color, remove from the oven.
As the brussels sprouts are roasting, make the balsamic glaze in a smaller skillet on the stove. Add the balsamic vinegar and maple syrup to the pan over medium-high heat. Bring the mixture to a boil then reduce to a simmer until it reduces down to a thick syrup.
Serve on a plate with the balsamic glaze drizzed over top, sprinkle with finely shredded parmesan cheese.