Preheat oven to 425 F. Grease a baking sheet.

Finely chop onion and celery. Add 1 tablespoon of olive oil to a pan over medium heat. Add chopped onion and celery and cook until soft and fragrant, about 3-5 minutes. Add to a large bowl and set aside.

Roughly chop salmon filets. Add chopped salmon to the bowl with onion and celery and add in beaten eggs, breadcrumbs, parsley, mustard, salt and pepper. Mix well to combine.

Using your hands, form mixture into 4-5 round patties, firmly packing them together.

Add remaining olive oil to a pan over medium heat. Add the salmon cakes and cook for about 2-3 minutes on each side, until golden and crispy.

Transfer salmon cakes to the baking sheet and finish cooking in the oven for 5-7 minutes, or until an internal temperature of 145 F is reached.