Preheat the grill. In a large mixing bowl, mix meat with basil leaves, red chili pepper, and 1 1/2 tablespoons of olive oil. Season with salt. Cover and refrigerate for 10 minutes.
In a large bowl, gently toss zucchini and tomatoes with 2 tablespoons olive oil, lemon juice, salt, and vinegar.
Divide meat mixture into 8 portions and flatten with your hands to make a patty. Grill hamburgers until meat is cooked through, turning once, about 2 minutes each side.
Grill zucchini and tomatoes, turning them frequently until zucchini softens and both zucchini and tomatoes are browned on both sides.
To serve, place hamburger between grilled vegetables with or without toasted bread or buns.