On a clean wooden cutting board, chop up the salmon filet into small flakey bits OR place chunks of salmon into a food processor and slightly pulse until salmon is in flakey bits. Do not over-process!
In a large mixing bowl, mix the salmon flaky bits with, chopped peppers, green onions, capers, garlic, Italian parsley and Pecorino Romano cheese.
In a separate medium mixing bowl, whisk together the egg(s), Dijon mustard, mayonnaise, lemon juice, lemon zest, salt and pepper.
Add this egg-mustard-mayonnaise mixture into the large mixing bowl with the salmon mixture.
Gently, but and thoroughly blend the salmon mixture with the egg-mustard-lemon mixture.
Gently mix in the Italian breadcrumbs.
Divide the entire salmon mixture into 4 equally sized balls.
With damp hands, pat each ball into 1-½ inch-thick patties.
Cover loosely with plastic wrap and refrigerate at least 30 minutes.
Preheat the grill.
Grill until browned on each side, because these are so thick and the burgers feel springy in the center and not soft, it took 10 minutes on each side.