Steam or boil the sweet potato until tender, then mash until smooth. Let it cool a moment.
Poach or bake the salmon until just cooked through, then flake it into pieces. You want small, tender chunks, not big flakes.
In a large bowl, combine the mashed sweet potato, flaked salmon, egg, breadcrumbs, parsley, Dijon mustard, salt, pepper, and lemon zest if using. Mix gently until everything comes together. If the mixture looks a bit loose, add a teaspoon more breadcrumbs.
Divide the mixture into four portions. Shape each into a patty about 3/4 inch thick. Chill for about 10 minutes if you have time; it helps them hold together while cooking.
Heat the olive oil in a nonstick skillet over medium heat. Add the patties and cook for 4–5 minutes on each side, until golden and crusty on the outside and cooked through inside.
Serve immediately with a squeeze of lemon, a dollop of yogurt or tartare sauce, and a side of greens or salad. Leftovers can be kept in the fridge for a day or two and reheated gently.