Preheat broiler on high, with oven rack 5 to 6 inches from broiler. Line rimmed sheet pan with foil.
Drain liquid from mozzarella and pat dry with paper towels. Cut log into eight ¼ inch slices. You’ll need 4 slices for the burgers, plus 4 to 8 additional slices for topping the burgers.
Add ground turkey, basil, panko, egg, salt, pepper, vinegar, and parsley to a large mixing bowl. Grate the onion and garlic over the bowl to catch all the juice. Mix ingredients using your hands until just combined. Do not overmix.
Divide meat mixture into four equal portions. Form one portion into a patty around a piece of mozzarella, making sure that cheese is completely encased by meat. Each patty should be about 4 to 5 inches in diameter. Repeat process for the remaining meat, forming 4 patties total. Place patties on prepared sheet pan.
Broil burgers for 8 minutes until golden brown, flip over, cook for another 5 minutes or until burgers are cooked through. Internal temperature should be 165°F.
If desired, spread pesto on buns. Add burgers to buns, top with sliced mozzarella, tomato slices, and fresh basil. Serve immediately.
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Notes
Nutrition information is for burgers and toppings. It does not include buns.
If desired, omit the cheese stuffing. Serve the turkey burgers with suggested toppings.