Place the salmon and mashed potato into a large bowl.
Add the salt and pepper, and using a fork, press the salmon into small pieces. Mix the fish and potato together once the fish is completely taken apart.
Add the mayonnaise and mix well. Next add the chopped parsley, and make sure the mixture holds together.
Divide the mixture into 4 equal balls. (Or make 3 for larger burgers.)
Form each ball into a patty, about the size of a bun.
Once the olive oil is heated on medium high heat in a sautè pan, add the salmon patties. Cook for about 4 minutes or until golden brown, then flip to cook the other side. Remove and place on paper towel lined plate.
Depending on your preferences, you can choose how to assemble your salmon burger. I put a little lemon mayo on the bun, then some lettuce leaves, the salmon patty, more lemon mayo (see recipe in notes.) I then added avocado slices, and a large slice of tomato.
You can omit any of the toppings, or make your own creation using your choice of sauce, lettuce and veg.