The total cooking time (including prep) for this dinner is 15-20 minutes. The cost of the ingredients less the wine, butter and seasoning is $7.00 to $9.00.
Start by sautéing carrots and leeks over medium heat in 1tbs of butter, 1/3 cup of white wine and a pinch of salt for 2-3 minutes. This will soften the vegetables and create a base to place your filet. Just prior to adding the salmon in the pan, squeeze the juice of 1/2 of a lemon and let it sit for a minute then add with the lemon juice skin-side down in the pan. Place 1/2 a tbs of butter on the top of the filet and cover the pan. After approximately 3 minutes flip the salmon so the skin is facing up and cover.
After 2 minutes uncover the pan, remove it from the burner and let it rest for 3-4 minutes. The fish will continue to cook in its own heat and absorb the flavors of the lemon wine and butter. The meal below was also accompanied by couscous and steamed broccoli, but use whatever you like.
Note: I was not able to figure out how to effectively remove the bones from the filet so next time I will ask if my grocer will do this for me or show me how.