Preheat grill to medium heat and set for indirect grilling.
Brush 1 tablespoon oil over chicken. Season on all sides with 2 tablespoons Sazonador Total. Grill covered over indirect heat, flipping once, until cooked through and registers 155 (breasts) and 165 (thighs) on instant read thermometer, about 40 minutes. Grill over direct heat for 5 minutes if needed, for additional browning.
Meanwhile, heat 1 tablespoon oil in large skillet over medium heat. Add onion and cook until softened, 5 minutes. Add tomatoes, vinegar, pepper, 1/4 cup water and 1 tablespoon Sazonador seasoning. Cook, stirring, over medium high heat, until tomatoes just burst, 5 to 6 minutes. Remove from heat and stir in basil. Serve with chicken and top with cheese, if using.
Note: You can omit the cheese from this recipe if you wish.