Preheat the oven:
Preheat to 400°F (200°C). Line a baking sheet with parchment paper for easy cleanup.
Prepare the vegetables:
Toss the potatoes, carrots, and broccoli in olive oil, salt, and pepper. Spread them evenly on the baking sheet and roast for 10 minutes.
Make the garlic butter sauce:
In a small bowl, whisk together melted butter, minced garlic, lemon juice, and paprika.
Add the salmon:
Move the vegetables slightly to make room for the salmon fillets. Place the salmon skin-side down, then brush generously with the garlic butter sauce.
Roast everything together:
Return the pan to the oven and bake for 12–15 minutes, or until the salmon flakes easily with a fork and the vegetables are tender and golden.
Serve and garnish:
Drizzle any remaining garlic butter from the pan over the top, sprinkle with fresh parsley, and serve with lemon wedges.