Heat oil in a medium pot over medium heat. Add the curry paste and fry, stirring constantly, until the oil begins to separate from the paste — about 8-10 minutes. The edges of the paste will look like they're glistening with their own oils.
Pour in half the coconut milk and stir well to combine with the fried paste. Cook for 5 minutes, then add the remaining coconut milk, fish sauce, and sugar. Bring to a gentle simmer (not a rolling boil). Taste — it should be balanced between salty, sweet, and slightly spicy. Adjust as needed.
Gently add the fish pieces into the simmering curry. Cook for 6-8 minutes until the fish reaches an internal temperature of 145°F and flakes easily with a fork. Do not stir too aggressively — you want to keep the fish intact.
Remove from heat and stir in lime juice and Thai basil leaves. Serve immediately over jasmine rice, spooning extra curry sauce over each portion.