1. Make the mayonnaise. Pulse the egg yolks, mustard, lemon juice, and sugar in a food processor until well combined. With the machine running, pour in the oil in a thin stream. Stir in the dill and season with salt and pepper. Transfer to a bowl, cover, and refrigerate.
2. Parboil the potatoes in boiling salted water for 5 minutes. Drain and cool. Peel and shred on a box grater.
3. Combine the grated potato, salmon, scallions, parsley, egg, and lemon zest in a medium bowl. Season with salt and pepper. In a shallow dish, combine the bread crumbs with the dill and parsley.
4. Shape the potato mixture into 6 cakes and coat in the bread crumbs. Heat the oil in a large nonstick frying pan over medium-high heat until shimmering. Add the cakes and fry, turning once, about 5 minutes, until golden on both sides. Transfer to paper towels to drain.
5. Serve hot, garnished with the lemon wedges, and serve the mayonnaise on the side.