Melt butter in a 12-inch saute pan over medium-low heat. Increase the heat slightly and add the onion, celery, and 1/2 teaspoon kosher salt; sweat for 5 to 7 minutes. Add garlic and cook for an additional 1 to 2 minutes. Reduce the heat to low and add the artichoke hearts, bread crumbs, lemon zest, remaining 1/2 teaspoon kosher salt, pepper, and oregano. Continue cooking for 2 to 3 more minutes. Remove from the heat and set aside.
Place the 4 cups rock salt on a sheet pan with sides and spread evenly. Set oysters atop the salt and divide the bread crumb mixture evenly among them. Place in oven and bake for 10 to 12 minutes. Bread crumbs should be lightly browned. Serve immediately.