Preheat your oven to 400°F (200°C).
In a large bowl, combine the shrimp, zucchini, olive oil, minced garlic, salt, black pepper, and paprika. Toss until everything is well coated.
Spread the shrimp and zucchini mixture evenly on a baking sheet lined with parchment paper.
Sprinkle the grated Parmesan cheese over the top of the shrimp and zucchini.
Roast in the preheated oven for 12-15 minutes, or until the shrimp are pink and cooked through and the zucchini is tender.
Remove from the oven and garnish with fresh parsley. Serve with lemon wedges on the side.