Use a pair of kitchen shears to cut through the backs of the shrimp and remove the veins. Place in a large casserole dish. In a medium bowl, combine the olive oil, lemon juice, marjoram, lemon zest, kosher salt and pepper. Whisk to combine, and drizzle the marinade over the shrimp. Cover the shrimp with plastic wrap and refrigerate for up to 2 hours, turning the shrimp to the other side after the first hour.
Preheat the grill to high heat. Remove the shrimp from the marinade and place on the grill. Cook for 3 1/2 minutes. Turn over and cook for another 3 1/2 minutes. Remove from the grill and place on a large platter. Season the shrimp with the sea salt and sprinkle with the chopped parsley. Serve with lemon wedges.