Chop salmon into ¼”-½” dice and place half of the diced Salmon in a food processor.
Add 1 tablespoon lemon juice and 1 teaspoon mustard.
Process, scraping down the sides as necessary, until smooth. Add the remaining salmon, bell pepper, shallot, salt and pepper and pulse until the mixture is combined but still chunky. Just a few pulses, you want to leave some of the chunks in the mixture.
Transfer the salmon mixture to a medium bowl. Add breadcrumbs and stir until combined.
Divide the mixture into 4 parts and form each part into a ball. Place each ball on a parchment lined plate, or small baking sheet. Gently push down each ball to form a 4” wide 1 1/2”-2” thick patty.
If you are making ahead of time, cover with plastic wrap and place in the refrigerator. If you are planning on cooking right away, place in the freezer while you prepare dressing.
Heat oil in a large cast-iron or nonstick skillet over medium-high heat.
Add the salmon cakes, leave as much space between each cake as you have available. Cook for about 2-3 minutes, or until browned, and flip cooking an additional 2-3 minutes on the final side. Transfer to a clean plate or baking sheet.