Combine artichokes, tomatoes, olives, red onions, parsley, marjoram, and lemon juice. Season with salt and pepper and mix well. Add the tuna and mix well, being careful not to break it up too much. Drizzle with olive oil and season.
Spread the tuna mixture onto the bottom half of the bread. Top with the upper portion of the bread, press down firmly and cut into sandwich sized pieces. Brush the outside of the bread with olive oil.
Have a large, cast iron skillet or a large griddle heated. Have a smaller cast iron skillet heating on the stove. Place the sandwich on the griddle or in the larger cast iron skillet. Top with the other hot skillet and cook just until both sides are golden brown and toasted. Slice and serve.