Heat 1 tablespoon of olive oil in a skillet over medium heat. Add the minced onion, bell pepper, and celery with a pinch of salt. Cook until the vegetables are soft and translucent, about 5 minutes.
Stir in the capers and cook for an additional minute. Remove from heat and let the mixture cool completely.
In a large mixing bowl, combine the chopped salmon, cooled vegetable mixture, mayonnaise, ¼ cup bread crumbs, minced garlic, Dijon mustard, cayenne pepper, and seafood seasoning. Season with salt and pepper to taste.
Cover the mixture with plastic wrap and refrigerate for 1 to 2 hours. This step helps the flavors meld and makes the mixture easier to form into patties.
After chilling, divide the mixture into four equal portions and form them into patties. Sprinkle the remaining tablespoon of panko bread crumbs over both sides of each patty.
Heat the remaining 2 tablespoons of olive oil in your skillet over medium heat. Cook the patties for 3-4 minutes on each side, or until golden brown and cooked through.