Preheat the oven to 400°F (205°C) and line a small baking sheet with foil.
Add the roughly chopped basil leaves to a mortar and pestle and pound the leaves until they turn into a wet paste. Add the green curry paste and mash until mixed together. Set aside in a bowl.
Cut the salmon into 4 fillets. Place on the lined baking sheet and pat the tops dry with a paper towel. Sprinkle with the kosher salt.
Bake for 8-10 minutes until mostly cooked through.
Meanwhile, heat the coconut oil in a large deep pan over medium heat. Add the ginger, garlic, and curry paste. Toss around for about 2 minutes until fragrant and the paste starts to dry out.
Gradually stir in the coconut milk to dissolve the paste then add the kaffir lime leaves, brown sugar, and fish sauce. Bring to a boil over medium-high.
Once boiling, reduce to medium and stir in the bell peppers and shallots. Simmer for 5 minutes until the peppers and shallots are slightly tender but not soggy.
Reduce to low heat and stir in the ⅔ cup of Thai basil until wilted. Nestle the salmon into the curry.
Spoon the sauce over the salmon and let it cook for 2-5 minutes until the salmon is fully cooked through the center.
Serve warm with rice, chopped cilantro, and sliced red chiles.