Whisk the eggs in a bowl and set aside.
In a large pan over medium high heat, add the onion, water, soy sauce and mirin. Give it a stir and bring it to a boil.
Add in the unagi and chopped green onion. Cover, and turn down the heat to low medium heat. Let the unagi cook for 5-10 minutes, until it becomes soft.
Uncover, and turn the heat to low. Pour in the egg in a circular swirling motion. Cover, and cook for a few minutes until the eggs are half cooked. Remove from heat.
Mix the rice with the furikake and place the unagi and eggs on top of the rice, followed by some chopped green onion and seaweed strips. Mix and enjoy!