In a large saucepan, add the mirin, soy sauce, lime juice, and ginger. Combine well and turn on medium heat.
Once the sauce starts simmering, add the salmon fillets with the flesh side turned down on the sauce. Cook for 5 minutes.
Rotate the fillets to sides every 5 minutes until the fish has cooked for a total of 15 minutes.
Add green onions and sesame seeds to the sauce and simmer for 5 more minutes. The sauce should be thickened by now.