Heat a pan and add 4 tablespoons of oil. Place the salmon and add a pinch of salt. Fry for about 2-5 minutes on each side, or until it is cooked to your liking. Transfer to a plate.
In the same pan, add 4 tablespoons of oil and the green curry paste. Fry for about a minute until fragrant. Add the ginger, lemongrass, and kaffir lime leaves (if using), and mix.
Pour in the coconut cream, stir well, and let it cook for 2 minutes. Add the brown sugar and lime juice, and mix until the sugar is dissolved. Add the green beans and simmer for 4 minutes.
Place the salmon on top of the sauce and beans. Cook for an additional 4 minutes or until the salmon is heated through and the beans are tender. Garnish with fresh cilantro leaves.