Preheat the oven to 375°F (190°C) and lightly grease a baking dish.
Butterfly the shrimp by slicing along the back without cutting all the way through. Arrange them in the baking dish with the cut side facing up.
Cook the butter, onion, celery, and garlic in a small skillet until softened. Transfer to a bowl and mix with the breadcrumbs, Parmesan, parsley, Old Bay seasoning, lemon zest, lemon juice, and broth until the stuffing is moist.
Divide the stuffing evenly among the shrimp, gently pressing it into each butterflied shrimp.
Brush the tops with melted butter and bake until the shrimp are pink and the stuffing is lightly browned.
Finish with fresh parsley and serve immediately with lemon wedge