To cook the onions and tomatoes, prepare a charcoal or gas grill so that the coals or heating elements are medium hot. Off the heat, lightly spray the grate with vegetable oil spray.

Slice the onions and tomatoes crosswise about 1/3 inch thick. Drizzle them with the olive oil and season with salt and pepper. Grill the onion slices for 3-4 minutes, turning once. Keep on the grill until softened. Grill the tomato slices on one side only for 2 minutes. Reserve to use as garnish.

To make burgers, in a small saute pan, heat the butter over medium heat until bubbly. Add the onion and garlic and saute, stirring occasionally, for about 4 minutes, or until soft and translucent. Set aside to cool slightly.

In a large bowl, combine the turkey, Worcestershire sauce, parsley, salt, thyme (if using), and pepper. Add the onion and garlic and mix well with your hands. Form the mixture into 8 patties, each 3/4 to 1 inch thick and about 3 1/2 inches in diameter.

Grill the burgers for about 6 minutes. Turn and grill for 4 to 5 minutes longer, or until cooked through. Brush each burger with barbecue sauce and grill for 2 minutes longer.

Serve topped with the grilled onions and tomatoes.