Make the chimichurri. In a bowl, stir together parsley, oregano, garlic, shallot, and red pepper flakes. Add olive oil, red wine vinegar, lemon juice, salt, and pepper.
Taste and adjust acidity and salt. Let it sit for at least 10 minutes so the flavors meld.
Season the steak. Pat the steak dry. Season both sides with salt and pepper.
If you have time, let it sit at room temperature for 20–30 minutes to cook more evenly.
Optional quick marinade. Spoon 2 tablespoons of chimichurri over the steak and rub it in. Set aside while you prep the salad, or marinate in the fridge up to 2 hours. Do not marinate overnight; the acids can toughen the meat.
Prep the salad base. In a large bowl, combine greens, tomatoes, red onion, and cucumber. Toss with a light drizzle of olive oil, a squeeze of lemon, and a pinch of salt.
This seasons the greens before the steak hits the plate.
Heat the pan or grill. Use a heavy skillet (cast iron is best) over medium-high to high heat, or preheat a grill to high. Add 1 tablespoon oil to the pan if using a skillet.
Sear the steak. Cook skirt or flank steak about 3–4 minutes per side for medium-rare, depending on thickness. For NY strip, 4–5 minutes per side. Target 130–135°F for medium-rare, 140–145°F for medium.
Rest and slice. Transfer steak to a cutting board and rest 5–10 minutes.
Slice thinly against the grain to keep it tender.
Assemble. Top the salad base with sliced avocado and warm steak. Spoon chimichurri over the steak, then add extra around the salad as a dressing. Sprinkle with feta or Parmesan if using.
Finish with flaky salt and fresh pepper.
Serve. Bring the remaining chimichurri to the table so everyone can add more. This is a sauce-forward dish—don’t be shy.