Mix marinade ingredients. Put ⅓ of the marinade in a shallow dish with the chicken, turning to coat. Reserve the other ⅔ for the sauce. Let the chicken sit in the marinade while you prepare the rest of the meal and wait for the grill to be ready.
Drain chicken and discard that marinade. Lightly salt and pepper each side of the cutlets to taste. Grill indoors, outdoors, or sauté in a skillet over medium heat until done, flipping once. If using a skillet, don’t crowd the pan--work in batches instead.
Make the sauce: in your smallest saucepan, bring the reserved marinade to a simmer. Stir in the cornstarch slurry. Cook, stirring, just until thickened.
Serve the chicken over rice and drizzle a spoonful or two of the sauce over the top.