In the bowl of a food processor, combine all sauce ingredients. Blend or pulse until the herbs and garlic are very finely chopped and sauce is smooth.
Divide sauce into two parts. Put 2 Tablespoons of sauce in a large mixing bowl (to add to the salmon patties). Refrigerate all remaining sauce to use on top of the burgers).
Wipe out the bowl of the food processor. Add salmon to the food processor in two batches and pulse until it forms pieces about the size of peas. Transfer each batch of chopped salmon to the bowl with the 2 Tablespoons of sauce. Add panko, mustard, salt, and chili powder. Gently stir until evenly combined.
Line a small sheet pan or plate with parchment or wax paper.
Form salmon mixture into 4 even patties. (To prevent sticking, wet your hands with some water or a bit of cooking oil before shaping the patties.)
Spread patties out in a single layer on prepared sheet pan or plate. Refrigerate for at least 30 minutes and up to a day (cover if refrigerating for more than 30 minutes).
Cook salmon patties in a well-oiled skillet over medium heat until patties are cooked all the way through, about 5 minutes per side.
Toast hamburger buns.
Spread toasted buns with reserved sauce and top with salmon patties, greens, sliced avocado, and other toppings. Enjoy!