To prepare aioli, combine first 3 ingredients in a small bowl; set aside.
To prepare cakes, combine salmon and next 5 ingredients (through mustard) in a medium bowl. Divide salmon mixture into 8 equal portions, shaping each portion into a (1/2-inch-thick) patty. Dredge patties in 1/2 cup breadcrumbs.
Heat oil in a large nonstick skillet over medium-high heat. Place patties in pan; cook 3 minutes on each side or until lightly browned and heated through. Serve aioli over salmon.