Preheat oven to 350°F. Place tomatoes and juices on a rimmed baking sheet and use your hands to break tomatoes into 3/4-inch pieces. Drizzle with 2 tablespoons oil and bake until thickened, 30 minutes, stirring every 10 minutes

Meanwhile, in a colander, toss eggplant with 1 1/2 teaspoons salt. Let sit 20 minutes, then squeeze out excess liquid. In a large Dutch oven or heavy pot, heat 4 tablespoons oil over medium. Add onion and cook, stirring occasionally, until translucent, 5 minutes. Add garlic and cook until onions and garlic are soft, 5 minutes. Add peppers and cook, stirring, until crisp-tender, 4 minutes. Season with salt and pepper.

Add tomatoes, eggplant, zucchini, bay leaf, and marjoram to pot. Cook, stirring occasionally, until mixture comes to a simmer. Reduce heat to medium-low, partially cover, and cook at a gentle simmer until vegetables are tender but not mushy, 15 minutes. Season to taste with vinegar, salt, and pepper. Remove bay leaf before serving.