Bring a large pot of water to a boil. Add a generous handful of Kosher salt to the boiling water.
Prepare the leeks. Jump here to learn how to clean them.
Melt 3 tablespoons of butter in a large skillet on medium-high heat and allow it to bubble so that its water content evaporates. Add the leaves of 3 sprigs of fresh thyme and allow to cook for a minute or so.
While this is happening, completely paper towel-dry your piece of salmon. Just before adding the salmon fillet, season it with salt and freshly-cracked black pepper. Add the salmon, pretty side first. You should hear a happy sizzle when the salmon hits the pan. Cook the salmon for 3 minutes and then flip and cook the other side for an additional 2-3 minutes, depending on how firm you want your salmon flakes to be.
Remove the salmon and place on a plate. Allow it to cool for a few minutes and then flake it with a fork. You can also use your hands for this as well.
Now, add the washed and drained leeks into the pan and mix thoroughly. Cook covered for 5 minutes, mixing the leeks halfway. Them lower the flame to medium and continue cooking for 15 more minutes, occasionally stirring.
When the leeks are 10 minutes or so from being done, add the spaghetti to the boiling water and cook according to their directions. When nice and al dente, or cooked but firm, drain them very well in a colander. Add most of the cooked spaghetti back in the pasta pot and pour the cooked leek mixture on top, along with the remaining 4 tablespoons of butter. Then pour the remaining cooked spaghetti in the skillet where the leeks have cooked to sop up any additional condiment stuck to the pan. Pour that back into the pot as well. Add the flaked salmon pieces and mix very well.
Arrange on your plate and sprinkle feta cheese and fresh-cracked pepper on top. Serve immediately.