1. In a large bowl, mix the salmon with the potatoes, onion and parsley. Season with salt and pepper to taste. Divide the mixture into 12 equal portions and roll each into a ball. Flatten each of the balls into a round cake.
2. Dip each cake into the egg then into the bread crumbs.
3. In a large skillet, melt the butter in the oil over medium high. Add the salmon cakes, 4 at a time, and cook until they are golden brown. Drain on paper towels. Serve the salmon cakes with the lemon wedges.