Peel the potatoes and grate on a wide-tooth side of a box grater or using the shredding disk of a food processor. Squeeze the moisture from the potatoes. (I like to wrap in a clean tea towel and literally wring out the excess moisture. Then I break up the clump with my clean hands for easy mixing later.)
Place the chopped chives in a medium mixing bowl.
Dry the salmon fillets thoroughly. Season with salt and pepper.
Place the potatoes in the bowl with the chives. Add the mayonnaise, season with salt and pepper, and stir to combine.
Scoop the potato mixture in equal portions over of each salmon fillet. Press it into the fish so that it is evenly distributed.
Heat a large sauté pan over medium heat. Add the olive oil and warm.
Once the oil is hot, carefully add the salmon fillets to the pan, placing the potato side down. Gently press down on the fillets to help the potato mixture adhere to the fish.
Sear the salmon until you can see that the potatoes are turning golden brown, about 3-5 minutes. Using a fish spatula or other big spatula, gently flip the fillets and cook until the sides look cooked through (or to your prefer degree of doneness), another 3-5 minutes.
Transfer the potato-crusted salmon to a serving platter or dinner plates, and enjoy!
