Place unagi on a lined baking sheet and cook in the oven for 5-8 minutes or until hot. Turn on the broiler and broil for 1 minute. Remove from oven and keep warm.
Heat 1 tablespon oil in a non-stick saute pan over medium heat. Whisk eggs and add soy sauce, mirin, sake, and sugar. Pour egg mixture into hot pan. Cover and let cook undisturbed for 2-3 minutes. The eggs should still be wet but set. Remove from heat.
Portion rice into 2 bowls and top with sweet simmered eggs and unagi. Finish with avocado slices, chopped scallions, and nori. Sprinkle togarishi on top if desired.
Notes
You can find unagi in the frozen section of Asian markets.