Put a quarter of the salmon and the mustard in a food processor. Blend until the mixture becomes an even paste. Add shallot and the remaining salmon and pulse until the mixture comes together but pieces of salmon still remain.
Scrape the mixture into a mixing bowl and add bread crumbs, capers and salt and pepper. Stir with a wooden spoon until evenly combined. Shape into 2 patties. Refrigerate (covered) until ready to cook.
Add the butter or olive oil to a skillet over medium-high heat. Cook the burgers for 2-3 minutes on each side, until cooked through. Serve on buns topped with any of the above toppings (we used cucumber slices, cilantro leaves and mashed avocado).