Start by washing and chopping your vegetables: broccoli, green beans, and zucchini. Grate the fresh ginger and set it aside. Cut the fish into bite-sized pieces.
In a large pot or Dutch oven, pour in the full-fat coconut milk along with the green curry paste. Stir them together over medium heat until combined and bubbling gently.
Add the grated ginger and fresh lime juice to the pot. Stir well to incorporate these fresh flavors into the curry base.
Add the chopped broccoli, green beans, and zucchini to the curry, cooking for about 5-7 minutes until they begin to soften.
Gently add the pieces of white fish to the pot. Drizzle in the fish sauce, if desired, and adjust seasoning with sea salt. Simmer for another 5-10 minutes until the fish is cooked through.
Ladle the curry into bowls and top with coconut milk yogurt and chopped chives for garnish.