I believe you're describing Chazuke (also called Ocahzuke). The salmon version is called Sake Chasuke (Sake meaning salmon, here, not rice wine). There is also a rice-and-egg porridge called Zosui.

1986):

Divide the rice among four deep bowls. Dry roast sesame seeds in dry skillet until golden, and crush them coarsely (in a suribachi, or a blender or with a heavy knife) and sprinkle them over the rice. Dry roast the nori by waving it over a gas or electric burner for up to a minute; fold and tear the sheet into 20 small rectangles and place 5 in each bowl of rice. If making sake chazuke, remove skin and bones from the salmon and break it into little chunks; divide it among the 4 bowls. Garnish each bowl with a little coriander and a small dab of wasabe. Pour 1/2 cup of very hot tea over each bowl and serve immediately.

(Jessica Litman)