In a bowl, toss peeled and deveined shrimp with olive oil, paprika, garlic powder, salt, black pepper, cayenne (if using), oregano, and thyme. Mix until evenly coated. Let sit for 10–15 minutes to marinate.
Heat a grill or grill pan over medium heat. Cook shrimp in a single layer for 2–3 minutes per side, until pink, opaque, and lightly charred. Don’t overcrowd the pan.
In a small bowl, whisk together mayonnaise, sour cream, parsley, minced garlic, salt, black pepper, and lemon juice until smooth. Chill for 5–10 minutes, if possible, to let flavors blend.
Arrange grilled shrimp on a platter or over greens. Drizzle with creamy sauce or serve the sauce on the side for dipping.