Cut the beef tenderloin into medallions about three quarters of an inch thick. Sprinkle with salt and pepper. Drizzle liberally with oil. Mix well. Place in a covered bowl and leave to marinate in the fridge for 30 minutes.
Take the meat out of the fridge. Remove the cover to allow the meat to go back to room temperature.
Fire up the grill (we used a stovetop grill). Ultra high heat is required. Brush or spray lightly with oil.
When the oiled grill starts to smoke, lay the beef tenderloin medallions in a single layer about two inches apart. Grill for two to three minutes per side depending on the doneness that you prefer.
Take the grilled beef tenderloin off the grill, transfer to a chopping board, cover loosely with foil and leave to rest for ten minutes.
Meanwhile, lower the heat of the grill to medium. Heat both sides of the tortillas.
Slice the beef tenderloin across the grain to about one-fourth to one-third inch thickness.
Assemble your tacos. Place a tortilla (or two) on a plate, arrange beef tenderloin slices on top and drizzle with chimichurri.
Serve the beef tenderloin and chimichurri verde tacos with shredded lettuce and chopped tomatoes on the side.