How to Make It
Preheat oven to 425 F. Place salmon skin side down on a rimmed baking sheet, season with salt and pepper, and bake until opaque, 8 to 10 minutes; let cool 10 minutes. Break salmon into large pieces, discarding skin, and transfer to a medium bowl.
Stir together mayonnaise, capers, and parsley in a small bowl. Add ¾ cup of the panko and ½ cup of the caper mayonnaise to salmon and stir gently to blend, keeping larger pieces of salmon intact. Shape mixture into 4 4-inch patties. Press remaining ¼￼ cup panko evenly on tops and bottoms of patties.
Heat oil in a large nonstick skillet over medium-high. Cook patties until golden brown, 3 to 4 minutes per side. Serve over romaine with tomatoes and cucumber, with remaining caper mayonnaise on the side.