1. Take the salmon out of the refrigerator 30 minutes before cooking to bring it to room temperature.
2. Open the can of coconut milk without shaking it first. Pour in the heavy cream that has separated and risen to the top. Reserve the cream in a small bowl. Pour the rest of the fine coconut milk and reserve it separately.
3. In a large sauté pan, heat the coconut cream over medium-low heat. Add the curry paste and whisk until the mixture is smooth and simmering. Add brown sugar and stir until dissolved. Add the clear coconut milk, water and fish sauce and bring to a boil, stirring once or twice. Add salmon fillets in a single layer, reduce heat to low, cover and simmer for 5 minutes. Flip the salmon, cover and cook for 2 more minutes. Scatter the snow peas around the salmon, dip them in the liquid, cover the pot and cook until the snow peas are bright green and the salmon is cooked through, about 2 minutes more. Remove the pan from the fire.
4. Transfer the salmon to warm dinner plates or shallow pasta bowls. Stir the lime juice, green onions and cilantro into the curry sauce. Drizzle the curry sauce and snow peas around the fillets, spreading the sauce and peas evenly. Serve immediately.