Wash the rice until the water runs clear. Drain and let sit for 30 minutes prior to cooking.
Place the rice and water in a heavy, deep, medium-sized saucepan with a well-fitting lid. Boil vigorously, uncovered, for 12 to 15 minutes, stirring occasionally. To keep from boiling over, tap the top of the pan a number of times with a spoon. Most of the water should disappear – if it evaporates too quickly, turn down the heat during the last few minutes of cooking to avoid burning.
Pour in the unagi sauce and mix well, then turn heat down to medium-simmer, cover the pan, and cook for 5 minutes. Add the eel slices, cover again, and simmer for a further 5 minutes. Turn off heat and let sit, covered, for 5 to 10 minutes.
Meanwhile, prepare the stock. Heat water and stir in the dashi until dissolved. Add soy sauce and sake and adjust seasoning.
To serve, mix the eel into the rice and serve in individual bowls. Pass the stock, green onion, and wasabi separately, allowing each person to mix in as they desire.