Heat a charcoal or gas grill or a grill pan to medium-high. Brush zucchini and onion with 1 tablespoon extra-virgin olive oil and sprinkle with salt and freshly ground black pepper. Grill for 2 to 3 minutes per side until tender and nicely charred. Remove and let cool slightly. Place zucchini and onion in a blender or food processor with the tomatoes, bread, 1 tablespoon olive oil, vinegar, and garlic. Cover and blend until smooth, adding water if necessary to thin (blend in batches, if necessary). Transfer to a serving bowl.
Serve immediately or chill up to 2 hours before serving. Garnish with parsley.