Salt the salmon well and let it sit on the counter while you chop all the vegetables. Heat the olive oil in a saute pan over medium-high heat. When the oil is hot, pat the salmon dry with a paper towel and set the portions, skin side down, on the hot pan. As soon as they are all set down, jiggle the pan a bit to let them move. If they don't move, just leave them. NOTE: you want to put the fish skin side down regardless of whether the skin is still there or not.
Let the salmon sear. You want it to sound like bacon sizzling in the pan, maybe a little bit more energetic than that. Use a spoon to baste the top of the fish with the hot olive oil until the flesh turns opaque. After about 5 minutes, check to see if the fish is ready by jiggling the pan again. If the portions move, you are good to go. If not, carefully try to lift them with a spatula. If they are stuck to the pan, leave them. Continue cooking for a minute or two more, then try again. They will lift up easily when you have a perfect sear.
If you are using thick salmon portions like the ones in the picture, you will want to flip your fish and cook it a few minutes on the other side. The way to do this is to flip one piece, jiggle the pan so that pieces slides around a little, then do the next piece. This way they will release from the pan faster than the first side, and this prevents you from overcooking the fish. Only cook the fish for a minute or two on this second side. NOTE: This is not needed for thin portions.
When the fish is ready, move it, crispy side up, to a cutting board and grind black pepper over it.
Add 1 tablespoon of butter to the pan, along with the shallots. Let this cook a minute, then add the capers and lemon zest. Mix well, let this cook about 30 seconds, then add the white wine. Use a wooden spoon to scrape up any browned bits from the pan. When this is done, add the lemon juice and the parsley. Turn the heat to low.
Now, add 1 tablespoon of butter to the sauce and swirl the pan until it incorporates. Repeat this with the rest of the butter. You can in fact add up to a half stick of butter this way, and it's amazing, but very rich. Serve by putting a portion on each plate and pouring some sauce over each one.
NOTE: If you are serving this with grits, polenta or mashed potatoes, make them first and keep it warm while you make the fish.