Remove the salmon from the refrigerator 30 minutes before cooking to bring it to room temperature.
Open the can of coconut milk without shaking it. Spoon out the thick cream that has separated and risen to the top. Set the cream aside in a small bowl. Pour off the remaining thin coconut milk and reserve it separately.
In a large sauté pan, warm the coconut cream over medium-low heat. Add the curry paste and whisk until smooth and the mixture comes to a simmer. Add the sugar and stir until dissolved. Add the thin coconut milk, water, and fish sauce and bring to a simmer, stirring once or twice. Add the salmon fillets in a single layer, turn the heat to low, cover, and simmer for 5 minutes. Flip the salmon, re-cover, and cook for 2 minutes longer.
Scatter the snow peas around the salmon, submerging them in the liquid, re-cover the pan, and cook until the snow peas are bright green and the salmon is cooked through, about 2 minutes longer. Remove the pan from the heat.
Transfer the salmon to warmed dinner plates or shallow pasta bowls. Stir the lime juice, green onions, and cilantro into the curry sauce. Spoon the curry sauce and snow peas around the fillets, dividing the sauce and peas evenly.
Serve and enjoy!