Start by chopping the broccoli, green beans, and zucchini. Make sure to wash them thoroughly and cut them into bite-sized pieces. Grate the fresh ginger and set it aside.
In a large pot or Dutch oven, pour in the can of full-fat coconut milk. Heat it over medium heat until it begins to simmer.
Once the coconut milk is simmering, add the green curry paste. Stir well to combine.
Add the grated fresh ginger and lime juice to the pot. Stir everything together.
Toss in the chopped broccoli, green beans, and zucchini. Stir to coat the vegetables in the rich curry sauce. Let them cook for about 5-7 minutes until they become tender but still crisp.
Cut the white fish into large chunks or fillets. Gently place the fish into the pot, making sure it's submerged in the curry. Let it cook for about 5-8 minutes, or until the fish is opaque and easily flakes with a fork.
Taste your curry and add fish sauce (if using) and sea salt according to your preference.
Ladle the Green Fish Curry into bowls. Top with a dollop of coconut milk yogurt and a sprinkle of chives for a fresh finish.