In a clean large mixing bowl, combine the cubed fresh salmon, soy sauce, and mayonnaise. Mix the ingredients well so the salmon is coated completely. Set this mixture aside in the fridge.
Next, combine the cooked rice, salt, and rice vinegar in a separate bowl. Again, mix the ingredients well so the salty-sour flavors are evenly distributed. Again, set it aside.
At this point, you can preheat the oven to 400⁰F.
Place the nori sheets on a dry chopping board. Cut them into 4 equal squares. If you are using large nori sheets, just cut squares that are small enough to perfectly fit into a muffin cup.
Press each square into a cup of a muffin tin. Work carefully because you don't want the sheets to crack.
First, add about 2-3 tablespoons of your vinegared rice mixture. Then, top each cup with a couple of tablespoons of the salmon mixture. Don't overfill the cups.
Repeat this assembly process until all of your rice and salmon mixtures have been used. Season all of the cups with some sesame seeds.
Place the salmon sushi cups inside the oven and leave them to bake for 15 minutes.
Once baked, remove them from the oven and let them rest for 5 minutes. Top the cups with green onions and serve immediately.