Melt the butter in a frying pan and saute the chopped onion over low heat until soft and translucent for 10 minutes. Set aside and cool.
In a food processor pulse the salmon fillet until roughly minced.
In a large bowl mix together the minced salmon, cooked onions, dry breadcrumbs, parsley, dill, lemon zest and juice, egg, salt and pepper.
Set the working surface for shaping the salmon fishcakes. You will need the fishcake mixture, a small bowl with dried breadcrumbs, a small ice cream scoop or a large spoon and a cutting board for the fishcakes.
Scoop the salmon mixture the size of a golf ball, roll it in your hands then flatten it slightly and dip in the breadcrumbs to coat the fishcake entirely. (See photos in the post.) Repeat until the salmon mixture is gone. You should have approximately 12-14 fishcakes. Put them in the freezer for 20 minutes to firm up.
Fry them in hot olive oil over medium heat for 3-4 minutes on each side until crispy on the outside and cooked all the way through. Place them on a paper towel lined platter to drain the excess oil.