Combine all your basil butter ingredients in a mixing bowl or food processor and set aside.
Bring your salmon to room temperature to ensure it doesn't stick to your pan. Then brush with olive oil and salt and pepper your salmon on both sides.
Heat up your oil in preferably a cast iron pan. Make sure to use a high smoke point oil. Let the oil heat on high heat for 4 minutes or so. You want to make sure the oil is very hot to get that nice sear.
Bring the heat down to medium high. If you are using skin on salmon, place your salmon down on the skin side first. Sear for about 3-5 minutes if you are using no skin and 5-7 minutes if you are using skin on salmon.
Flip and cook for an additional 3-4 minutes.
Bring your heat down to medium and remove the excess oil leaving about 1 tbsp. Add in your basil butter. Continuously spoon the butter over your salmon for about 30 seconds to finish cooking it.