Place the shallot and cilantro or parsley into the work bowl if a food processor– pulse until finely chopped. Now add in the fresh salmon and smoked salmon, pulse until just chopped– not a paste. Remove to a bowl.
Whisk the egg with the Dijon mustard, and pour into the bowl with the fish, stir well to completely combine, cover and set in the fridge for at least 30 minutes (up to the night before).
When you are ready to saute, grab the fish mix and stir, shape into 4 burgers.
Get a griddle or large saute pan good and hot over medium heat. Spray the pan with non-stick spray or drizzle in oil, lightly salt the burgers and place in the pan to cook, without moving until golden brown on one side, about 4 minutes.
Spray the top with more non-stick spray (or oil), salt and carefully flip over– cook until some white proteins are released from the burger and the other side is golden, about 2-3 minutes longer.
Serve at once on Kaiser rolls with lettuce, mayo, etc.