Step 1 Spray a large non-stick frying pan with olive oil and set over medium–high heat. Add salmon fillets and cook for 2–3 minutes per side, or until tender. Flake cooked salmon finely with a fork and transfer to a large bowl.
Step 2 Spray a small non-stick frying pan with olive oil and set over medium heat. Add half of the shallots to pan; cook until soft. Add ginger to pan; cook for a few minutes. Add shallots and ginger to salmon bowl.
Step 3 Add mashed sweet potato to salmon bowl with lime zest and breadcrumbs; season with black pepper and mix well. Wet hands to shape mixture into 4 patties, then refrigerate for 5 minutes. Meanwhile, make coleslaw: Mix all ingredients with remaining shallots in a salad bowl.
Step 4 Spray a large non-stick frying pan with olive oil and set over medium–high heat. Cook patties for 2–3 minutes per side, or until cakes are slightly golden.
Step 5 Serve ginger salmon cakes with green coleslaw.