Heat the olive oil in a large skillet over medium heat. Add the chicken pieces and season with salt and pepper. Cook the chicken for about 6-8 minutes, stirring occasionally, until the chicken is browned and cooked through. Remove the chicken from the skillet and set it aside.
In the same skillet, add the chopped onion and sauté for about 3-4 minutes, or until softened and translucent. Add the minced garlic and ginger, and cook for another 1-2 minutes until fragrant.
Stir in the curry powder, ground cumin, paprika, and turmeric. Cook for another 1 minute to toast the spices and bring out their full flavor.
Pour in the coconut milk, soy sauce, fish sauce (if using), and brown sugar. Stir well to combine. Bring the mixture to a gentle simmer and cook for 5 minutes, allowing the flavors to meld together.
Add the cooked chicken back into the skillet, along with any juices. Stir to coat the chicken in the sauce and cook for an additional 5-7 minutes, until the chicken is heated through and the sauce thickens slightly.
Stir in the fresh basil leaves, letting them wilt into the sauce. Taste the sauce and adjust seasoning with more salt, pepper, or soy sauce if needed.
Serve the spiced coconut basil chicken over cooked jasmine or basmati rice. Garnish with fresh lime wedges on the side for a burst of citrus.
