Begin by cooking the salmon. You can either poach it in simmering water for about 10 minutes, or bake it in a preheated oven at 375°F (190°C) until cooked through and easily flaked, which should take about 15 minutes.
Once the salmon is cooked and cooled, flake it into small pieces using a fork and place it into a large mixing bowl.
Add the breadcrumbs, mayonnaise, egg, dill, lemon zest, lemon juice, minced garlic, salt, and pepper to the bowl. Mix everything together gently until well combined. Ensure not to overmix, as you want to keep some texture.
Using your hands, form the mixture into patties about 2 inches in diameter, and place them on a plate. You should yield around 8 cakes.
Heat olive oil in a large skillet over medium heat. Once hot, carefully place the salmon cakes in the skillet, cooking in batches if necessary to avoid overcrowding.
Fry for about 3-4 minutes on each side, or until golden brown and crispy.
Once cooked, transfer the salmon cakes to a paper towel-lined plate to absorb any excess oil.
Notes
Serve garnished with fresh dill and lemon wedges. Consider adding tartar sauce or lemon dill yogurt sauce for extra flavor.