1 cup plus 1 tablespoon mayonnaise
6 green onions (2 minced, 4 cut into 4-inch lengths)
1 tablespoon fresh lemon juice
2 teaspoons grated lemon peel
1/4 cup (packed) chopped fresh Italian parsley
1 1/4 pounds skinless salmon fillets, cut into 1-inch cubes
2 tablespoons Dijon mustard
1/2 cup panko (Japanese breadcrumbs) or fresh breadcrumbs made from crustless French bread
3/4 teaspoon salt
3/4 teaspoon ground black pepper
Whisk 1 cup mayonnaise, 2 minced green onions, lemon juice, and grated lemon peel in small bowl to blend. Season lemon mayonnaise to taste with salt and pepper and set aside.
Combine remaining 4 green onions and chopped parsley in food processor; blend until finely chopped. Add cubed salmon, Dijon mustard, and remaining 1 tablespoon mayonnaise. Using on/off turns, blend until salmon is coarsely chopped. Transfer salmon mixture to large bowl. Mix in breadcrumbs, 3/4 teaspoon salt, and 3/4 teaspoon ground black pepper. With moistened hands and using about 1/3 cupful for each, shape salmon mixture into 8 patties, each about 1/2 inch thick. Brush both sides of salmon cakes with olive oil.
Prepare barbecue (medium heat). Grill salmon cakes to desired doneness, about 3 minutes per side for medium. Divide patties among 4 plates. Serve lemon mayonnaise alongside.