Rub salmon skin with some oil and season salmon with salt and pepper.
Place salmon in the grill skin down and cook it, with the lid closed, just until it's opaque and firm to the touch. Depending on the thickness of salmon, it will take from 8 to 12 minutes.
Sauce:
Preheat a cooking pan over medium heat.
Slice shallots thinly and add them to the pre-heated pan. Add butter to the pan and stir as it melts. Let butter simmer and get browned. It won't take long, especially in a stainless steel pan.
Once butter is browned and gets a beautiful nutty aroma, add lemon and orange zest, minced basil, pinch of salt, and lemon and orange juices. Stir and let is simmer for just a couple of minutes. Take off heat.
Once salmon is cooked, pour sauce over the whole salmon.