For the chimichurri, combine all of the ingredients in a food processor. Pulse and taste for seasoning. Adjust if necessary. If the mixture is thick, add some more olive oil and vinegar until it turns out to your liking.
Poor half of the chimichurri in a bag or bowl and coat the steaks with the marinade. Marinate for at least 30 min up to overnight.
While it is marinating, make your sauce by combining the ingredients in a bowl. You can make this ahead of time (if you do, skip the feta until you’re about to serve it) to let the fennel absorb the lime juice. Or you can make it right before serving.
30 minutes before cooking your steak, remove it from the fridge and let it come to room temperature. He’s a skillet on high heat. Season with oil. Sere the steak for 2 to 3 minutes per side and continue to cook on medium heat until it reaches 125F internally (or to your liking.) Let the steak rest 10-15 min before slicing.