Preheat oven to 425°F. Line a rimmed baking sheet with foil and lightly oil it.
Whisk melted butter, olive oil, honey, Cajun seasoning, lemon juice, garlic, paprika, cayenne, salt, and pepper in a bowl.
Pat shrimp dry. Toss with about two‑thirds of the sauce until evenly coated.
Spread shrimp in a single layer on the pan. Spoon any extra sauce from the bowl over top.
Bake 6–8 minutes, until pink and just cooked through.
Switch to broil and cook 1–2 minutes to lightly caramelize the glaze.
Drizzle with remaining sauce, sprinkle parsley, and serve hot.