Begin by marinating the salmon: For the marinade, mix together the miso, mirin, and sugar in a shallow pan. Turn the fillets over in this mixture, so that it's coated on all sides. Cover and refrigerate for two hours.
When the salmon is almost done marinating, cook the rice: In a three quart saucepan, bring a cup and a half of water to a boil. Add the rice and half a teaspoon of kosher salt. Cover and simmer for 16 minutes. Then, remove from the heat and let sit, covered, for ten minutes.
Also, cook the eggs: In a small pot, bring one inch of water to a boil. Add the eggs and simmer covered for 8 minutes. Drain the eggs, and let them sit in a bowl of ice water for 12 minutes. Peel under cold running water.
For the Salmon: Heat a grill pan on medium heat, and brush with vegetable oil. Brush the marinade off the salmon and grill on both sides for about four minutes per side, or until cooked through.
Place some rice in each bowl and top with salmon, halved eggs, carrots, squash, and edamame.