Preheat your oven to 400°F and line a large baking sheet with parchment paper.
Pat the shrimp completely dry with paper towels and place them in a large mixing bowl.
Whisk together melted butter, olive oil, garlic, salt, pepper, and oregano in a small bowl. Pour over the shrimp and toss to coat.
Sprinkle grated parmesan over the bowl and toss gently until the cheese clings to the shrimp.
Spread the shrimp in a single layer on the prepared baking sheet, ensuring they do not touch.
Bake for 8 to 10 minutes until opaque and the cheese is melted. Garnish with parsley and serve with lemon wedges.