To begin, prepare the sauce (tare) by combining soy sauce, mirin, sake, and sugar in a small saucepan. If you prefer a bit of a zing, add the grated ginger. Simmer the mixture over medium heat for about 10 minutes, stirring occasionally, until it thickens slightly into a glaze. Set aside to cool.
Preheat your oven to 400°F (200°C). Lightly oil a baking sheet or broiler pan. If you're using an outdoor grill, ensure it is clean and preheated to medium-high heat.
Place the eel fillets on the prepared baking sheet, skin-side down. Brush the eel generously with the tare sauce. This will help the fish caramelize and develop a rich, sweet flavour during cooking.
Place the eel in the oven and bake for 10 minutes. Alternatively, you can grill the eel on a charcoal grill for an even smokier flavour, turning occasionally to ensure even cooking. Keep brushing with the tare sauce to build up a glaze.
After 10 minutes, switch your oven to broil, or if using a grill, increase the heat to high. Broil the eel for another 5-7 minutes, watching closely to avoid burning. The eel should develop a slightly crisp, caramelized exterior while remaining tender inside.
While the eel is broiling, reheat the tare sauce briefly on the stove. This will give it a fresh shine when brushed over the cooked eel.
Once the eel is cooked through and caramelized, remove it from the oven or grill. Brush the fillets one last time with the warm tare sauce to enhance the flavour and add a beautiful gloss.
To serve, slice the unagi into portions and place over steamed white rice in bowls for a traditional unagi donburi presentation. Garnish with sliced green onions and a sprinkle of toasted sesame seeds for added texture and aroma. Enjoy with extra tare sauce on the side, if desired.