Hmm so I have been looking up sushi combinations and it seems typical sushi does not get frosted with cheese.
There are exceptions however, such as this offering from Bangkok's Gojuu Sushi "The most eye-catching dish is the Special Roll Cheese Lava . Four aburi salmon maki are blanketed in a thick coat of melted mozzarella. The sushi is subsequently drizzled with both soy sauce and a piquant Japanese BBQ sauce. A liberal sprinkling of ebiko (shrimp roe) and chopped scallions cap off the dish.""