Preheat the oven to 425°F (220°C). Lightly grease a small baking dish.
In a large bowl, combine the breadcrumbs, minced garlic, dried oregano, parsley, lemon zest, red pepper flakes, kosher salt, black pepper, and Pecorino Romano cheese. Drizzle in the olive oil and mix until the breadcrumbs are evenly moistened.
Pat the shrimp dry with paper towels and arrange them in a single layer in the greased baking dish. Squeeze lemon juice over the shrimp, then pour the dry white wine around them.
Spoon the breadcrumb mixture over the top of each shrimp, pressing gently so it adheres. Drizzle the melted butter evenly over the topping.
Bake at 425°F (220°C) for 12–15 minutes, until the shrimp are opaque and cooked through. If the topping isn’t golden brown, broil for an additional 1–2 minutes to crisp it up.
Sprinkle with extra fresh parsley and serve immediately with lemon wedges on the side.