Grind the salmon. Place cubed salmon in the bowl of a food processor fitted with blade attachment. Pulse about 5-6x, or until the fish is pretty finely chopped, but not a paste. Transfer to a large mixing bowl.
Add remaining ingredients. To the salmon, add ½ cup sour cream, ¼ cup chives, ¼ cup tarragon, ¼ cup fresh dill, 1 Tbsp chopped capers, 2 tsp Dijon mustard, 2 Tbsp fresh lemon juice, and the zest of 1 lemon. Season with 1 tsp Kosher salt and ¼ tsp freshly ground black pepper. Use a spatula or your hands to gently combine all the ingredients.
Form the salmon burger patties. Divide the salmon mixture into 6 equal portions, then use your hands to shape into uniform patties. If not cooking immediately, cover with plastic wrap, then refrigerate for up to 8 hours.
Make the tarragon mayonnaise. Place ¾ cup mayo, ¼ cup chopped tarragon, and 2 tsp white wine vinegar in a small bowl, then stir well. Season with ¼ tsp Kosher salt, taste, and adjust seasoning as needed. Set aside.
Cook the salmon burgers. Preheat a nonstick skillet (or grill) over medium-high heat, then coat with nonstick cooking spray. When hot, add salmon burgers and cook for 2-3 minutes per side, working in batches as needed, or until an internal temperature of 120F is reached.
Garnish, then serve. Place a generous amount of tarragon mayo on both sides of the burger bun, then place a heaping mound of salad greens on the bottom bun. Place a cooked salmon burger patty on top, along with any burger toppings you like. Finish by placing the top of the burger bun on the patty, then serve immediately!