First, make the chimichurri sauce: Combine all ingredients in a bowl and whisk together well with a fork. Set aside.
Heat a medium-large frying pan over medium heat. Add the coconut oil and swirl it around until it is evenly coated.
Carefully lay as many plantains on the pan flat as you can, without them touching. They should each have a little space in between. Let them cook on one side for about 1-2 minutes, just until it gets a golden yellow, before flipping and cooking the other side for 1-2 minutes. Remove to a plate when done. Repeat with any remaining plantains.
You could sprinkle the plantains with a pinch of pink salt while cooking to eat on their own, or serve plantains with the chimichurri sauce.