Combine the seasonings and fish
In a food processor, combine the ginger and green onions and process until finely chopped, stopping once or twice to scrape down the sides of the work bowl. Sprinkle the salmon with the cornstarch and add to the processor with the egg white, a pinch of salt, and the fish sauce. Using quick pulses, process until the mixture resembles coarsely ground meat. Do not overprocess the mixture or the cakes will be heavy.
Form and chill the cakes
Divide the salmon mixture into 8 equal portions. With moistened hands, gently shape each portion into a patty about ½ inch (12 mm) thick. Transfer to a plate, cover with plastic wrap, and refrigerate for 5–10 minutes.
Cook the cakes
In a large frying pan over medium heat, warm the 1 tablespoon oil. Add the salmon cakes and cook until golden brown on the first side, about 3 minutes. Turn, adding more oil if needed, and cook until the cakes are slightly springy to the touch and have lost their raw color in the center, 2–3 minutes longer. Transfer to plates and sprinkle with the sesame seeds. Serve, passing the soy sauce, chile sauce, and lemon wedges at the table.