Preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper or foil.
Pat the shrimp dry with a paper towel and place them in a large mixing bowl.
In a small bowl, combine melted butter, olive oil, minced garlic, lemon juice, and zest. Mix until well blended.
Pour the garlic butter mixture over the shrimp, tossing to coat them evenly.
Add grated Parmesan cheese, salt, black pepper, red pepper flakes (if using), and half of the chopped parsley to the shrimp. Toss again to ensure everything is evenly distributed.
Spread the shrimp out in a single layer on the prepared baking sheet, ensuring they aren’t overlapping.
Roast the shrimp in the preheated oven for 8–10 minutes, or until they turn pink and opaque.
If desired, broil the shrimp for an additional 1–2 minutes to achieve a golden, crispy finish on the Parmesan topping.
Remove from the oven, garnish with the remaining parsley, and serve immediately with lemon wedges.