Place the turkey, sun-dried tomatoes, water, grated cheese and basil or parsley, if using, in a large bowl. Gently mix with a fork or your fingertips until blended; do not overmix. Shape the mixture into 4 patties about 1/2-inch thick.
Preheat the George Foreman Grill (or charcoal grill). When hot, place patties on. Cook for 4 minutes. If not done, flip over and cook for another couple of minutes.
While cooking, toast buns. When done, put burgers on buns, top with cheese.