Preheat the oven to 425°F (220°C).
Line a large sheet pan with parchment paper or aluminum foil for easy cleanup.
In a large bowl, combine the broccoli florets, 2 tablespoons of olive oil, minced garlic, 1/2 teaspoon kosher salt, and 1/4 teaspoon black pepper. Toss until the broccoli is evenly coated.
Spread the broccoli in a single layer on one side of the prepared sheet pan.
Place the salmon fillets skin-side down on the other side of the sheet pan.
Drizzle the remaining 1 tablespoon of olive oil over the salmon fillets.
Sprinkle the salmon with the remaining 1/2 teaspoon kosher salt, 1/4 teaspoon black pepper, and smoked paprika.
Arrange lemon slices evenly over and around the salmon fillets.
Place the sheet pan in the preheated oven and roast for 15 to 20 minutes, or until the salmon flakes easily with a fork and the broccoli is tender and slightly caramelized.
Remove from the oven and sprinkle chopped fresh parsley over the salmon and broccoli before serving.