Cut the fish into 8 oz portions. For most Sockeyes this will be either in three or four portions depending on the size of the fish. Since Sockeyes are much smaller and thinner than King salmon I prefer to cut the meat on the bias or angle instead of straight down. Once the fish has been properly cleaned and portioned, keep it cold in the refrigerator until needed and start the sauce.
To make a Beurre Blanc (White Butter) sauce, it's best to begin a large skillet-12" to 14" works best. If you only have a 10" this will still work, it will just take a little longer. What you are looking for is a large cooking surface since this will be a triple reduction.
Start with the white wine, minced shallots and white pepper. You should have enough wine just to cover the shallots in the skillet/sauté pan. With the pan over high heat reduce the wine to au sec or almost gone. The mixture should be kind of sludgy. Not totally dry, but not too wet.
Add the clam juice and reduce the the same way to au sec or sludgy again. (Again, not totally dry, but not too wet.)
Add the cream and follow the same procedure until the cream has reduced until it thinly covers the bottom of the pan and the bubbles from the cream start to get slightly bigger.
Reduce the heat under the skillet/sauté pan and add the softened butter one or two pats at a time. Whisk the sauce until all of the butter has been incorporated. Do not leave the process at this time, commit to whisking until the end.
Once all of the butter has been incorporated, add the dill and dijon mustard. Whisk in and taste for salt. Add salt if needed.
Classically the sauce would be strained at this moment and reserved. I like the rustic version of leaving the shallots in and bumping up the brightness of the sauce with a little lemon juice. Keep the sauce warm until the fish is cooked.
In a hot skillet or sauté pan, add oil. Allow the oil to heat up for a few seconds and then add the fish (inside down first). This will be the presentation side and will look best with a brown crunchy top.
As the fish cooks, notice a slight brown edge will form around the fish after about 8 minutes. With one hand, lift the skillet by the handle to gather the oil on one side. With the other hand, lift the salmon with a spatula and flip over to the raised side of the pan with no oil. Gently lower the pan back down and let the oil run back over the fish. This will prevent splashing the oil out of the pan.
Cook the fish a few more minutes until the center of the fish has firmed up and is no longer soft or spongy. With an instant read thermometer, 135-140 degrees is the correct temperature for just medium.
Remove fish from skillet and serve with mustard dill beurre blanc.