To make the balsamic reduction, add balsamic vinegar and brown sugar to a small saucepan over medium heat. Bring to a slight boil and reduce by half, about 6-8 minutes; set aside and let cool.
Place brussels sprouts into a 3-qt slow cooker. Stir in olive oil and season with salt and pepper, to taste. Top with butter.
Cover and cook on low heat for 3-4 hours or high for 1-2 hours.
Serve immediately, drizzled with balsamic reduction and topped with Parmesan.