Preheat oven: Preheat your oven to 400 degrees Fahrenheit. Line a rimmed baking sheet with parchment paper.
Dry the shrimp: Thoroughly pat the peeled shrimp completely dry with paper towels to ensure they roast instead of steam.
Coat with oil: Place the dried shrimp in a large mixing bowl. Pour the olive oil over them and toss well.
Add seasonings: Sprinkle the minced garlic, parmesan, salt, pepper, and smoked paprika into the bowl. Toss again until evenly coated.
Arrange on pan: Spread the mixture onto the prepared baking sheet in a single layer, ensuring no pieces overlap.
Roast: Bake for 8 to 10 minutes, or until the shrimp are opaque pink, form a loose C-shape, and the cheese is melted.
Garnish and serve: Remove from the oven, immediately sprinkle with fresh parsley, and serve warm with lemon wedges.