Begin by making the miso marinade: Combine the mirin and sake in a small saucepan and bring to a gentle boil for about 30 seconds. Reduce the heat to low and whisk in the miso paste and then the sugar to fully combine and dissolve the sugar. Transfer to a metal bowl to cool.
Dry the salmon with paper towels, but don't rinse. Place the fillets skin-side up in a shallow-rimmed dish and pour on the marinade so it touches all sides of the fish. Cover tightly with plastic wrap and refrigerate for 1 to 3 days.
To cook: Preheat the broiler. Scrape off excess marinade and place the salmon fillets skin-side down on a parchment-lined baking sheet. Broil for 8 to 15 minutes, or until the internal temperature reaches 125 to 130° F for medium or 140° F for well-done.
Garnish with toasted sesame seeds and sliced scallions. Serve immediately.