Cut the salmon into large pieces, and put about a quarter of the salmon into a food processor, along with 2 teaspoons Dijon mustard. Turn on and off a few times, you do not want a paste.
Add the remaining salmon pieces and green onions. Turn on and off to combine, again you do not want a paste.
Transfer mixture to a bowl and add; capers, lemon juice, tarragon breadcrumbs, and salt and pepper. Gently fold the ingredients together until well mixed.
Form into 6 sliders and refrigerate for at least a half hour, or up to two hours.
Heat a 12-inch cast-iron skillet over medium-high heat for a few minutes, add the olive oil. After an additional few minutes add the salmon sliders to the pan and cook for about 3 minutes per side, or until done. Be careful not to over cook.
Serve in a dinner bun with with tomato, lettuce, and tarragon Dijon mustard.