Make the pistou: place the garlic cloves in a small food processor, and mince. Add the basil and process again to chop, then add ⅓ cup of the olive oil, salt and pepper and blend until it becomes a bright green sauce.
Season the steak generously with salt and pepper. Heat a large heavy skillet, such as cast iron, over medium-high heat. Add 1 tablespoon olive oil, and when the oil is hot, sear the steak for 3 to 4 minutes on each side for medium rare. Remove the steaks to a cutting board and let them rest for 5 minutes before serving.
While the meat is resting, in a large bowl combine the remaining 2 tablespoons olive oil, vinegar, salt and pepper. Stir to combine, add the lettuce and toss.
Serve the filets with a drizzle of the pistou on top, and a couple of handfuls of the dressed mixed greens. Pass the rest of the pistou on the side for extra drizzling.
Notes
What is Pistou?
Pistou is an Italian word that often is basically interchangeable with pesto (pistou is French, pesto Italian), though often pistou is made with a looser consistency than pesto, which can be quite thick. In a pistou sometimes the pine nuts and/or Parmesan are omitted, resulting in a simpler basil, garlic and olive oil sauce. That’s the drizzle you’re going for here, just a pop of herb-infused green olive oil to brighten up that perfect little filet.