Preheat a grill to high. Position a dutch oven on the grate, add 3 tablespoons olive oil, the crushed garlic and shrimp tails, cover and cook for 5 minutes. Using a slotted spoon, discard the garlic and the shrimp tails. Add the zucchini and bell pepper, season with salt and pepper and cook for 5 minutes. Stir in the broth and simmer for 15 minutes; add the corn and thyme during the last 5 minutes of cooking.
Meanwhile, toss the shrimp with 1 tablespoon olive oil and season with salt and pepper. Thread onto skewers and transfer to the grate; grill, turning once, until opaque, about 3 minutes. Remove from the skewers and stir into the soup.
Brush the bread with the remaining 2 tablespoons olive oil. Arrange on the grate and grill until toasted, about 3 minutes. Rub the toasts with the remaining garlic clove. Serve with the soup.