How to Make It
Finely chop salmon on a cutting board; place in a medium bowl. Add chives, salt, pepper, and 4 tablespoons of the mayonnaise; stir to combine. Shape mixture into 8 (2 1⁄2-inch-wide) patties. Place breadcrumbs in a shallow dish. Place each patty in breadcrumbs; press to coat all sides.
Heat oil in a large skillet over medium-high. Add patties to skillet; cook until golden brown and internal temperature reaches 130°F, about 3 minutes per side. Remove from skillet.
Whisk together parsley, buttermilk, soy sauce, lemon juice, sugar, and remaining 3 tablespoons mayonnaise in a small bowl.
Divide lettuce, snap peas, and radishes evenly among 4 plates. Top each with 2 salmon cakes; drizzle with dressing.