Make the chimichurri first. Mix all ingredients together in a bowl. Allow to sit for 5-10 minutes to release all of the flavors into the oil before using. Ideally you want to let it sit for more than 2 hours, if time allows.
You can also throw all the ingredients except for the olive oil in food processor and puree. Then slowly add olive oil until combined.
Salmon
Preheat oven to 400°F. In cast iron skillet or ovenproof skillet heat 2 tablespoon unsalted butter over high heat. Place salmon skin side down. Cook for 3 minutes to brown the skin and spoon some of the melted butter over the top of the fish as it cooks.
Transfer skillet to oven and roast until the fish is just cooked through, about 8-10 minutes. Serve with 2 tablespoon chimichurri over each piece of salmon.
Notes
Use wild salmon when possible. It is healthier for you and just tastes better.
For even crispier skin, lightly dust the skin side of the fillet with flour before placing them in the skillet.
Once salmon is added to the pan, cook undisturbed for 3 minutes so a nice crust forms before adding to the oven.
Don't add the chimichurri until after the salmon is cooked.
You know the salmon is done when it is opaque and easily flakes.