Get ready to have the best quesadilla of your life. What makes this recipe so different from others is the BBQ sauce along with the marinated chicken. When you put it into the tortilla your mouth gets hit with a flavor that it's never felt before.
Mince the garlic and grate the ginger using a fine holed cheese grater or box grater. In a small bowl stir together the brown sugar, soy sauce, garlic, ginger, some freshly cracked pepper (about 15 cranks of a pepper mill), and cooking oil. Place the chicken thighs in a shallow dish or a gallon size zip lock bag. Pour the marinade over the chicken and turn to coat. Cover the chicken and marinate for at least 30 minutes or up to a day (refrigerated).
When ready to cook the chicken, heat a large skillet over medium flame. Once hot, add ½ Tbsp cooking oil and swirl to coat the bottom of the skillet. Add half of the chicken pieces and let cook until well browned on each side and cooked through. Remove the cooked chicken to a clean plate, then repeat with the second batch.
Once all the chicken has been removed from the skillet, pour the leftover marinade into the skillet and allow it to come up to a boil. Whisk the marinade as it boils to dissolve any browned bits from the skillet. Let it continue to boil until it reduces to a thick glaze*. Turn the heat off, add the cooked chicken back to the skillet, and dredge it in the thick glaze. Garnish with sliced green onions and sesame seeds if desired.
*It is safe to cook used marinades as long as they come to a full boil, according to the FDA food safety guidelines. This thoroughly cooks the marinade, just like the raw chicken that was in it, to kill bacteria. The used marinade should be cooked immediately and should not be stored uncooked for later use. If concerned, double the marinade and use half for the chicken and reduce the other half in a small sauce pan before brushing it onto the chicken.