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 in a single layer on a large baking sheet.
Sprinkle the grated Parmesan cheese evenly over the top.
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.