Place the chicken in a bowl and mix with soy sauce, oyster sauce, salt, and black pepper. Cover and marinate for at least 1 hour, preferably overnight in the refrigerator.
Cook the jasmine rice according to package instructions. Keep warm until serving.
Heat a frying pan over medium heat with a little oil. Place the chicken skin-side down and cook until the skin is golden and caramelized. Flip and cook until the chicken is fully cooked (internal temperature 70°C / 158°F). Remove the chicken and keep warm in the oven at 90°C / 195°F while preparing the sauce.
Using the same pan, remove excess oil if needed, leaving enough for flavor. Fry the red curry paste in oil over low heat for 1 minute. Add the grated garlic and ginger, cook for another 1 minute. Pour in the coconut milk and chicken stock. Let the sauce simmer for 5 minutes. Season with fish sauce, lime juice, lime zest, brown sugar, and salt.
Spoon jasmine rice into bowls or onto plates. Slice the chicken and place it over the rice. Ladle the red curry sauce over the chicken. Garnish with fresh chili, cilantro, lime wedges, and chili oil. Serve immediately and enjoy.