In a small bowl, combine miso paste, mirin, and a splash of lime juice until smooth. Coat the salmon fillets evenly with this mixture and let marinate for at least 30 minutes.

Rinse the black rice under cold water until the water runs clear. Combine it with 2 cups of water in a saucepan, bring to a boil, then simmer for 25-30 minutes until tender.

Preheat the oven to 400°F (200°C). Place the marinated salmon skin-side down on a baking sheet and bake for about 12-15 minutes until opaque and flaky.

In a mixing bowl, toss diced cucumber with coconut milk and the remaining lime juice. Season to taste with salt and pepper.

Spoon a portion of black rice onto each plate, top with salmon, and serve the salad alongside. Add lime wedges for freshness.