Heat olive oil in a large skillet over medium heat. Add shallot and garlic and cook until soft and fragrant, about 3 minutes.
Sprinkle salmon fillets with salt and pepper on both sides. Place fillets, skin-side up, in the skillet; cook for 4 minutes. Flip salmon skin-side down and spread shallot and garlic over top. Add broccoli around the fillets, stirring to coat in oil. Squeeze lemon halves over salmon and broccoli.
Cover the skillet and steam until salmon is cooked through and flakes easily with a fork, about 5 minutes.