To make the Green Goddess Sauce: Combine the avocado, 2/3 cup Greek yogurt, 1/3 cup mayonnaise, garlic powder, 1/4 cup parsley, 1/4 cup basil, chives, 1/2 juiced lemon, 1/2 tsp salt, and 1/4 tsp pepper in a blender and blend until smooth. Set aside.
To make the Salmon Burgers: Cut the skinless, boneless salmon filet into small pieces. Add the salmon into a food processor and process 1-2 times (do not make it perfectly smooth). Add the 2 tablespoons Dijon mustard, 1 tablespoon mayonnaise, 1 tablespoon lemon juice, 1 tablespoon fresh dill, 1 teaspoon salt, and 1/4 teaspoon black pepper into the food processor. Pulse until ground, scraping down the sides as needed, ensuring to keep some texture and not turn it into a purée. Transfer the salmon mixture to a bowl. Pour in the 1/2 cup breadcrumbs and mix with a spatula to combine. Form the salmon mixture into 4-5 patties, about 1/2 inch thick. Place the patties on a parchment paper-lined plate, cover, and refrigerate for 15 to 20 minutes before cooking.
Heat 1 tablespoon of oil in a pan over medium heat. Once hot, add the salmon burgers and cook for about 3-4 minutes per side, or until golden brown. Gently flip the burgers and cook for another 3-4 minutes.
Serve the salmon burgers with the green goddess sauce, toasted buns, arugula, and slices of lemon.
