Heat grill or grill pan to medium-high. In a small pot over medium-low heat, combine ketchup, garlic, honey, vinegar and 2 tsp of the soy sauce. Bring to a simmer; cook 10 minutes. Set aside to cool.
In a bowl, combine turkey, 1/4 cup of the barbecue sauce, the parsley and remaining 1 tsp soy sauce. Form into 4 patties.
Lightly oil grill or grill pan. Grill burgers 5 minutes; flip and grill another 4 minutes, or until burgers reach 160° on an instant-read thermometer. (If adding cheese, place on burger after flipped.) Grill buns 1 to 2 minutes, until toasted. Serve with remaining barbecue sauce and Apple-Celery Slaw, if desired.