Stuff each pepper with cheese and a sprig of marjoram. Transfer stuffed pepper and pepper tops to a glass loaf pan.
Whisk oil, vinegar, garlic, salt, and pepper in a small bowl. Pour over peppers. Let marinate at room temperature 1 hour.
Preheat oven to 400 degrees. Place tops on peppers. Cook until cheese has melted and peppers are tender, 12 to 15 minutes. Let cool slightly. Serve with bread.