Prepare the rice according to the package directions; keep warm.
Heat your broiler.
Bring the water to a boil. Remove from heat and add the tea bags. Let steep. In a small saucepan, combine the rice vinegar, 1/2 cup sake, sugar, and ginger. Bring to a boil and let reduce by half. Stir in the brewed tea. Discard the tea bags and ginger.
Place the salmon filets skin-side down on a broiling pan. Broil 2 minutes. Meanwhile, mix together the miso paste and remaining sake to form a thick sauce. Spread the sauce over the salmon and broil another 3 minutes, or until the edges begin to brown. Lift the salmon from the pan, leaving the skin behind.
Stir the scallions and sesame seeds into the rice.
To serve, spoon a mound of rice into the center of four bowls. Ladle the broth around the rice. Top with salmon.