Fill a large pot with water and bring to a rolling boil over high heat. Place Brussels sprouts in water and cook for 2 minutes. Remove sprouts from water and transfer to ice water to cool. Drain and pat dry. Set aside.
Place onions in boiling water; cook until nearly tender, about 10 minutes. Remove from water, rinse with cold water, and pat dry. Set aside.
Melt butter in an ovenproof skillet over medium heat. Stir in Brussels sprouts and onions; toss with butter to coat. Stir in salt and black pepper; cook for 2 minutes.
Transfer skillet to the preheated oven and roast until golden and tender, 15 to 20 minutes. Garnish with lemon wedges and serve.