1. Heat broiler. Line a cookie sheet with foil. Place bell peppers on prepared sheet and broil six inches from heat source, turning occasionally, until evenly charred, 10 minutes. Wrap in foil; let stand until cool enough to handle. Remove the charred skins. Cut peppers in half; seed and cut into 1/4-inch strips.
2. Reduce oven temperature to 325 degree F. Heat 1 tablespoon oil in 12-inch skillet over medium-high heat. Add half the zucchini in single layer and cook, turning, until browned, 6 to 8 minutes. Sprinkle with 1 teaspoon marjoram, 1 teaspoon garlic, 1/4 teaspoon salt, and 1/8 teaspoon pepper. Cook 1 minute more, turning gently. Repeat with 1 tablespoon oil, remaining zucchini, marjoram, garlic, salt, and pepper.
3. Place basil leaves on cutting board, drizzle with 4 teaspoons oil and chop coarsely. Spread evenly on bottom of 3-quart shallow baking dish.
4. Toss artichokes in bowl with 2 teaspoons oil; arrange in single layer in prepared dish. Top with zucchini. Arrange tomato wedges on top of zucchini, overlapping slightly. Arrange pepper strips in a crisscross pattern over tomatoes. Sprinkle evenly with Parmesan and drizzle with remaining 2 tablespoons oil. Bake 45 to 55 minutes or until most of the liquid evaporates from the tomatoes and vegetables are browned. Serve warm or at room temperature. Makes 8 servings.