In a small bowl, toss squash and zucchini with 1 tablespoon olive oil and 1 clove garlic. Season with salt and pepper. In a separate medium bowl, toss bread cubes with remaining 2 tablespoons oil and 1 clove garlic. Season with salt and pepper.
Grill squash and zucchini mixture on tin foil over medium-high heat until veggies are slightly charred and tender. Lay bread cubes out on tin foil and toss frequently over medium-high heat until bread is charred and slightly crispy. Remove from heat and cool.
In a large serving bowl, combine lettuce, cucumber, tomato, grilled veggies, and grilled bread. Toss to combine and stir in basil and Parmesan. Set aside for a moment.
In a small bowl, whisk lemon juice, agave, mustard, and garlic until smooth. Drizzle olive oil into mixture, whisking constantly until dressing is smooth. Season dressing with salt and pepper to taste.
When ready to serve, drizzle dressing over salad and toss to combine. Serve salad immediately. Enjoy!