Combine all of the ingredients in a food processor or blender and process until smooth. Scrape down the sides when necessary, until feta is super creamy. Taste and adjust seasoning. Transfer to an airtight container and refrigerate.
To make salmon burgers stovetop:
To a food processor add ⅓ of the chopped salmon with the mayonnaise and mustard and pulse 8-10 times or until the texture looks similar to ground beef. Add remaining chopped salmon, pulse 3-4 times. You should see assorted textures.
Dump the mixture into a bowl and, with a spatula, fold in the breadcrumbs, scallions, garlic powder, onion powder, lemon pepper, black pepper, kosher salt, smoked paprika, celery seed, and lemon juice.
Divide mixture into four patties. Mold, transfer to a sheet pan and cover in plastic wrap. Place in fridge for at least 30 minutes (see notes).
Heavily spray grill pan or nonstick skillet with cooking spray and place over medium heat. Sear the patties for 5 minutes on each side. ￼
Spread whipped feta over toasted buns and top with salmon burgers. Continue to assemble with your favorite toppings like butter lettuce, red onion, whipped feta, tomato. Serve right away.