Make your tzatziki and set aside. This can be done up to three days in advance.
Blitz three quarters (maybe a little more) of the salmon in a food processor until chopped very fine or ground into a paste. (I know. "Salmon paste" doesn't sound very delicious. It will be.) Chop the remaining salmon into a small dice.
In a mixing bowl, mix the salmon, Dijon mustard, scallions, parsley, salt, black pepper, cayenne, and the juice of half a lemon until fully combined.
Form the salmon mix into 4 patties, pressing them together firmly. Lightly dredge each patty top and bottom with the breadcrumbs.
Heat a thin layer of vegetable oil in a large skillet over medium-high heat until the oil shimmers and a few breadcrumbs dropped into the pan sizzle. Lower the heat to medium, then fry the salmon burgers until nicely browned on each side and cooked just through, about 3 or 4 minutes per side. Drain on a paper towel-lined plate.
Serve hot with a generous spoonful of tzatziki on top, over warm buns or rolls. Cut the remaining half lemon into a few wedges and serve with the salmon burgers.
Disclaimer: Nutrition information is provided for courtesy purposes only, and is an estimate not verified by medical or nutrition experts. Read the full nutrition disclaimer.