Pulse salmon, parsley, mustard, capers, and salt in a food processor. Divide and shape into four patties.
In a large nonstick skillet, heat 1 tablespoon olive oil over medium-high heat. Cook salmon patties two to three minutes per side, until golden brown.
In a bowl, toss sugar snap peas with chives and juice from lemon, season with salt. Serve with salmon burgers. Optional: add a whole grain bun or side of quinoa.