Preheat your oven to 400°F (200°C). Line a large baking sheet with parchment paper for easy cleanup.
In a large bowl, combine the halved baby potatoes, broccoli florets, and cherry tomatoes. Drizzle with 2 tablespoons of olive oil, and sprinkle with garlic powder, paprika, salt, and pepper. Toss until the vegetables are evenly coated.
Spread the vegetable mixture in a single layer on one side of the prepared baking sheet. Place the salmon fillets on the other side of the sheet. Drizzle the remaining tablespoon of olive oil over the salmon and season with salt and pepper. Top each fillet with lemon slices.
Bake in the preheated oven for 20-25 minutes, or until the salmon is cooked through and flakes easily with a fork, and the vegetables are tender and slightly caramelized.
Remove from the oven and let it cool for a few minutes. Garnish with chopped fresh parsley before serving.