Slice the mini brioche buns and lightly toast them so they are warm on the outside and soft inside.
Drain the canned Alaska wild salmon well and gently flake it, maintaining some of its texture.
Finely chop the surimi, pickles, and piparra peppers into even pieces.
Mix the mayonnaise with the Dijon mustard. Add the surimi, canned Alaska wild salmon, pickles, and piparra peppers. Fold gently until a moist filling is obtained, taking care not to turn it into a paste.
Adjust the seasoning with salt only if necessary, considering the saltiness of the canned salmon, smoked Alaska wild salmon, and pickled ingredients.
Fill each mini brioche with the surimi and canned Alaska wild salmon mixture.
Top with a small slice of smoked Alaska wild salmon.