Prepare the teriyaki sauce: In a small saucepan over medium heat, combine the reserved 1/4 cup pineapple juice, soy sauce, rice vinegar, honey, garlic, and ginger. Cover and bring to a boil. Once boiling, remove the lid and cook for 1 minute, stirring constantly. While you wait for the sauce to boil, whisk the cornstarch and 1 tablespoon water together in a small bowl to create a slurry. Once the sauce is boiling, add the slurry, then stir to combine. Cook for 1 additional minute, until the sauce begins to thicken. Remove from heat.
In a large mixing bowl, combine the ground turkey, panko, garlic, ginger, black pepper, cilantro, and 3 tablespoons teriyaki sauce. Mix just until combined, and be careful not to compact the meat. Shape into four 3/4-inch-thick patties. Place in the refrigerator for 30 minutes.
Set aside some of the remaining teriyaki sauce for serving, reserving the rest for grilling. Preheat the grill to medium high and lightly oil the grates. Grill the rings of pineapple and red onion slices until caramelized and tender, about 3 minutes per side for the pineapple and 4 minutes for the red onion. Grill the burgers for 4 minutes on the first side, flip, then brush with sauce. Grill 4 minutes, then flip again and brush the other side with sauce. Continue cooking until the burgers are cooked through and reach an internal temperature of 160 to 165 degrees F, about 10 minutes total. Remove to a plate, cover, and let rest 5 minutes. If desired, grill the buns.
Serve the burgers inside of the buns, brushed with reserved sauce and topped with grilled pineapple and red onion.
Serving: 1patty with 1 pineapple ring, 1 thick onion slice, and a light brushing of extra teriyaki sauce, Calories: 254kcal, Carbohydrates: 25g, Protein: 23g, Fat: 7g, Saturated Fat: 2g, Cholesterol: 91mg, Sodium: 734mg, Fiber: 2g, Sugar: 13g