Heat half the sunflower oil in a wok over high heat. Stir-fry the chicken breasts until browned but still slightly pink in the center. Remove and keep warm.
Add the remaining oil and sauté the garlic, ginger, chilies, kaffir lime leaves, and onion for 2-3 minutes until fragrant. Stir in the mushrooms and carrot, cooking over high heat for 7-8 minutes until tender-crisp.
Return the chicken to the wok. Pour in the oyster sauce, soy sauce, fish sauce, and poultry stock. Simmer over high heat until the sauce thickens and coats the ingredients. Remove from heat, then gently fold in the bean sprouts and basil leaves.
Serve hot with steamed rice for a restaurant-quality Thai dish packed with bold flavors.