Prepare the Potatoes: Peel and boil the potatoes until tender, then mash them. Let the mashed potatoes sit and cool for a few minutes.
Make the Salmon Mixture: In a large bowl, combine the mashed potatoes, salmon, egg, lemon juice, lemon zest, flour, parsley or dill, salt, and pepper. Mix well until everything is combined.
Form the Cakes: Using your hands, shape the salmon mixture into patties, about the size of your palm. Dust each cake lightly with flour to help them crisp up during cooking.
Prepare the Salmon Cakes: In a large skillet, warm the olive oil over medium heat. Cook the salmon cakes for 3 to 4 minutes on each side until they achieve a golden brown and crispy texture. Once done, move them to a plate lined with paper towels to absorb any excess oil.
Prepare the Sauce: In a small bowl, whisk together the Greek yogurt, chives, pressed garlic, lemon juice, salt, and pepper. Adjust seasoning to taste.
Serve: Serve the salmon cakes hot with the chive and garlic yogurt sauce on the side. If desired, finish with extra parsley or serve alongside lemon wedges for a burst of flavor.