Preheat the oven to 425°F (220°C) and line a baking sheet with parchment paper if desired.
Wash, peel (if preferred), and cut the potatoes into small cubes. In a large bowl, toss the potatoes with olive oil, salt, black pepper, and paprika until evenly coated.
Spread the seasoned potatoes on one side of the prepared baking sheet in a single layer and bake for 25 minutes, stirring halfway through until golden brown and crispy.
While the potatoes are roasting, melt the butter in a medium saucepan over medium heat. Add the minced garlic and cook for 1-2 minutes until fragrant. Stir in the juice of one lemon and season to taste with salt and pepper.
Season the salmon fillets with salt and pepper. After the potatoes have baked for around 15 minutes, push them to one side of the baking sheet and place the salmon fillets in the cleared space.
Spoon the lemon butter mixture over the salmon fillets and add lemon slices on top. Place the broccoli florets on the same baking sheet, drizzle with olive oil, and season with salt and pepper.
Return the baking sheet to the oven and roast everything together for an additional 15-20 minutes or until the salmon is cooked through and the broccoli is tender.
Once done, remove from the oven and let rest for a couple of minutes. Garnish with fresh parsley if desired.
Serve the salmon alongside the crispy potatoes and roasted broccoli on plates.