Bring wine and 1 ½ cups of water to a simmer in a saucepan large enough to hold the salmon fillet. (A deep skillet is also fine.) The fillet should be just about covered with the liquid.
Add salmon and simmer gently for 8 minutes, or until cooked through. Feel free to turn it over as it simmers to make sure all sides are cooked through. Remove from pan and let cool, then pat dry.
Meanwhile, thinly slice shallot.
Add 1 tablespoon of butter to a small nonstick skillet over medium-high heat.
Add shallot and sauté until lightly browned, about 5 minutes. Let cool.
Whisk together the rest of the butter, Greek yogurt, Old Bay seasoning, lemon zest, lemon juice, and chopped chives.
Flake cooled salmon, removing skin, and stir gently into the butter mixture, along with the sautéed shallots.
Spread into a ramekin or another serving dish.
Chill for 30 minutes to allow the flavors to meld and the butter to firm up again.
Sprinkle with Old Bay seasoning before serving.
Notes
This is a great dish to make-ahead. Simply chill the rillettes in the refrigerator in their serving dish. It will keep for up to three days. Note that the Old Bay flavor begins to mellow after some time in the refrigerator, so you may want to garnish with extra seasoning before serving. Also, take out salmon rillettes about 15-20 minutes before you want to eat it, so that the butter has time to soften slightly. This will make for a tastier dip that’s easier to spread too.
Not overcooking the salmon is the key to this recipe. Make sure that your water is only at a simmer, and not fully boiling. Since you will end up flaking the entire fillet, you won’t ruin it by checking whether the salmon is cooked through. Just stick your fork into it and see whether the flesh flakes apart.