Melt butter in a frying pan. Place in buns face down until toasted to a golden brown, then remove.
Heat olive oil in a frying pan until hot then add desired number of salmon patties. Grind pepper over patties. Cover and continue to heat on medium.
Flip patty after it browns on one side. Grind pepper over the other side, then continue heating until equally browned.
Add aioli to lower bun before placing salmon patty. Next place a handful of arugula over the patty and freshen with a squirt of lemon juice before placing top bun.