1. Preheat oven to 425°F (240°C).
2. In a large pot of boiling salted water, parboil the whole potatoes for about 10 minutes. (Parboiling means boiling until a knife inserted indicates they are still a bit firm inside.) Remove from heat and let cool completely (so they will be less starchy and won't stick together). Once cooled, remove skins from the potatoes. In a medium bowl, grate the potatoes, then combine with the green onions, season with salt and pepper, and set aside.
3. Season the salmon with salt and pepper. In a large-ovenproof skillet on medium-high, heat the oil. Sear the salmon skin-side up for 2 minutes until browned.
4. Remove salmon from the pan and brush the seared side of the salmon with the mustard. Spread 1/4 cup of the potato and onion mixture on top of each fillet. (The mustard adds a nice flavor as well as adhering the potato to the fish.)
5. Return the salmon back to the skillet, potato side down. Cook until the crust is golden brown. Flip the salmon over and place the pan into the oven for 3 to 4 minutes, or until the fish is slightly pink in the middle.