Combine the ginger, garlic, lemon zest, salt and olive oil in a small bowl. Blot the fish dry with a paper towel and coat well with the ginger mixture. Place the fish fillets on a heatproof plate or a shallow dish for steaming, and set aside.
To make the turmeric rice, heat oil in a large pot on medium high, cook onion and garlic for about 3 minutes until softened. Stir in turmeric, thyme, bay leaf and carrots and cook for a minute.
Add the rice and stir until rice is fully coated with the yellow onion mixture. Add coconut milk, vegetable broth, cayenne pepper, and salt. Bring the rice mixture to a boil, cover and simmer on low for 50 minutes or until rice is tender. Remove from heat and keep covered for about 10 minutes. Fluff the turmeric rice with a fork, stir in chopped coriander and a squeeze of lime juice.
Steam the fish by resting the dish in a steamer or on a small rack over simmering water, cover and steam for 10 minutes, or until just cooked through (the fillets should look opaque and flake easily but remain moist). Using a spatula, transfer the fish to a serving dish. Pour any juices from steaming over the fish and add a squeeze of lemon over the fish. Garnish with coriander leaves and spring onions. Serve with turmeric rice.