Mix together mayonnaise, green onion, and dill. Set aside.
To make the burgers:
In a large bowl, mix together salmon, green onion, capers, egg, 2 tablespoons bread crumbs, dill, salt, and pepper. If mixture feels very wet, add additional bread crumbs. Form mixture into four patties. It should be wet but stay together easily.
Heat olive oil in a large skillet over medium high heat. Add patties and fry for about 4 minutes per side, until cooked through.
To assemble:
Toast rye bread and slather with mayonnaise. Add some greens, then slide the salmon burger on top. Top with a sprig of dill, if desired, and serve immediately.
Recipe by Things I Made Today at https://www.thingsimadetoday.com/2016/02/29/scandinavian-salmon-burgers/