Add chopped salmon into a food processor and pulse it several times. Scrape down the sides and repeat the process 3-4 times. We want a mixture with bits of fish instead of a mushy paste.
Dump the mixture into a bowl and, with a spatula, mix in the egg, mustard, scallions, cilantro, garlic powder, coriander powder, paprika, breadcrumbs, salt and pepper, and 1/2 tsp lemon juice.
Wet your hands and form 4 patties. Place the patties onto a wide surface, such as a large cutting board or baking sheet.
In that same pan, melt 1 1/2 tbsp butter and sear the patties for 5 minutes on each side. Take them out and place them onto a large, flat dish.
In a small bowl, whisk together sour cream, parsley, garlic, and the remaining lemon juice.
Melt the remaining butter in a grilling pan over medium heat. Sear the buns for 2 minutes or until they are charred a bit. Take them out of the pan.
Assemble the burgers: bottom bun, arugula, tomato slices, red onion slices, the patty, sauce, and the top bun. Serve these burgers right away!