Season the cubed cod with a pinch of salt and toss to combine.
Preheat a large heavy bottomed pan over medium-high heat. Add a spoonful of coconut oil followed by the green curry paste. Stir and cook for 60-90 seconds, scraping bottom of the pot with a wooden spoon.
Add in coconut milk. Stir and bring to a simmer, cook for 2-3 minutes. If desired, pulse mixture with an immersion blender to further puree paste. This step is optional.
Stir in the brown sugar, fish sauce, green beans and eggplant. Stir and bring to a simmer. Cover and cook for 3 minutes.
When the vegetables are about 60-70% cooked, add fish and gently stir to submerge. Cover and reduce the heat to low. Poach for another 3 minutes.
Serve over rice, top with a squeeze of lime juice and garnish with thai basil.