Preheat the oven to 425°F (220°C). Line a large rimmed baking sheet with parchment paper or lightly coat it with cooking spray.
Pat the fish fillets dry with paper towels. Check for pin bones and remove them with kitchen tweezers if necessary.
Place the broccoli florets and peeled garlic cloves in a large bowl. Mix the olive oil, lemon juice, salt, black pepper, and paprika in a small bowl. Toss the broccoli and garlic with about half of the seasoning mixture.
Spread the broccoli and garlic in a single layer on the prepared baking sheet. Roast for 10 minutes.
Brush the fish fillets with the remaining seasoning mixture. Remove the baking sheet from the oven and arrange the fish beside the broccoli without overcrowding the pan.
Bake for another 12 to 16 minutes, until the broccoli is tender and the fish is opaque, flakes easily with a fork, and reaches an internal temperature of 145°F (63°C).
Let the fish rest for 3 minutes. Sprinkle with chopped parsley, add an extra squeeze of lemon juice, and serve warm.
