In a medium bowl, combine 4 tablespoons of softened unsalted butter, 2 tablespoons of white miso paste, 1 tablespoon of brown sugar, 1 teaspoon of grated fresh ginger, and 1 clove of minced garlic. Mix until well blended and smooth to create the miso butter.

Place the salmon fillets skin-side down on a lined baking sheet or in a suitable oven-safe skillet. Evenly divide the miso butter mixture over each fillet, ensuring each piece is generously coated.

Preheat your oven to 375°F (190°C), then bake the salmon for 12-15 minutes until done, becoming opaque and flaking easily with a fork. For extra caramelization, broil for an additional 1-2 minutes.

For air frying, preheat to 400°F (200°C), line the air fryer basket with parchment, then cook the coated salmon fillets for 9-10 minutes without flipping.

Transfer the cooked fillets to a serving platter, drizzle remaining miso butter on top, and garnish with sliced green onions and sesame seeds. Serve with steamed rice or sautéed vegetables.