Adjust oven rack to the middle position and heat oven to 400°F.
Melt butter and sugar together in microwave.
Toss brussels sprouts, shallots, butter mixture, vinegar, salt, and pepper in a large bowl.
Scatter on rimmed baking sheet and roast until golden brown, about 30 minutes, shaking pan every 10 minutes to redistribute brussels sprouts.
Serve and enjoy!!