Place one chicken breast at a time in a zip-top bag and pound to an even thickness of about 1/2 inch; be careful not to puncture the bag. Repeat with the second breast. Seal the bag(s) and set the chicken aside.
In a medium bowl combine 1/4 cup low-sodium or gluten-free soy sauce, 1/4 cup unsweetened apple sauce, 1/4 cup finely chopped yellow onion, 1 tsp sesame oil, 1 tsp grated ginger, 1 tbsp light brown sugar, 2 crushed garlic cloves, 1 teaspoon red pepper flakes (optional), and 1 teaspoon sesame seeds. Stir until the brown sugar is dissolved.
Measure and reserve 1/4 cup of the marinade in a small bowl (this will be used for basting). Pour the remaining marinade into the bag(s) with the chicken, remove excess air, seal, and refrigerate for at least 1 hour.
When ready to cook, preheat a grill to medium-high heat and oil the grates lightly. Remove the chicken from the bag, letting excess marinade drip back into the bag; discard the used marinade that was in contact with the raw chicken.
Place the chicken on the preheated grill and cook for 2 to 3 minutes on the first side, until it releases easily from the grates. Flip the chicken.
Immediately spoon the reserved 1/4 cup of marinade evenly over the two breasts, then grill the chicken for an additional 2 to 3 minutes on the second side, or until cooked through (internal temperature reaches 165°F / 74°C or no pink remains).
Transfer the chicken to a plate and let rest for 3 to 5 minutes.
Sprinkle additional sesame seeds for topping and scatter the 2 thinly sliced scallions (white and green parts) over the chicken before serving.