Mix tomatoes, onion, garlic, basil leaves, oregano, and marjoram in an 8x8-inch baking dish; sprinkle with kosher salt and black pepper. Drizzle with olive oil and balsamic vinegar and toss ingredients to combine.
Roast in the preheated oven until the tomatoes and onion are soft and the juices turn brown and sticky, 20 to 30 minutes. Set aside to cool while you complete the remaining steps.
Place a Boston lettuce leaf onto 6 serving plates and sprinkle shredded romaine lettuce over each leaf. Divide the warm roasted tomato mixture among each salad; top salads with shaved Parmesan cheese. If any caramelized tomato juices remain in the pan, spoon over the salads.