Lay a large piece of plastic wrap on a work surface and place a sheet of nori in the center like a diamond, shiny side facing down. Using clean, wet hands, spread ⅓-cup rice in a thin, even, compact layer and form into a 4-inch square in the center of the diamond. Season with a pinch of salt.
Spread a generous layer of mayonnaise on top of rice, then arrange salmon, avocado, cucumber, and ginger on top in thin even layers. Season with togarashi and salt.
On another piece of plastic wrap, take ⅓-cup rice and pat into a 4-inch square. Flip onto the top of sandwich and peel away the plastic wrap. Tightly fold the bottom point of the nori diamond up over the filling, then the right point over the filling, then the top point and then the last point to make a neat, compact square.