Rinse and pat dry the shrimp with paper towels. Toss the shrimp with olive oil and Old Bay seasoning in a bowl. Thread the shrimp onto skewers and set aside.
Heat the grill pan over high heat. Lay each skewer on the pan and grill for 3 to 5 minutes per side, until the shrimp turn pink.
Dish out the shrimp, sprinkle with freshly chopped parsley, and serve immediately with fresh lemon juice squeezed on top.