Pat the filet mignon dry with paper towels.
Season generously with salt and black pepper.
Optional: Rub lightly with olive oil or a high-smoke-point oil.
Preheat a cast-iron skillet or heavy pan over high heat until very hot.
Sear the filets 2–3 minutes per side to form a deep brown crust.
Optional: Sear the edges briefly (10–20 seconds per edge).
Optional: Add 2–4 tablespoons butter, plus smashed garlic cloves and thyme/rosemary to the pan.
Baste by tilting the pan and spooning the melted butter over the filets for 30–60 seconds.
Check doneness with an instant-read thermometer:
120–125°F (49–52°C) for rare
130–135°F (54–57°C) for medium-rare
140–145°F (60–63°C) for medium
150–155°F (66–68°C) for medium-well
160°F+ (71°C+) for well-done
Optional oven finish if thicker:
Transfer to a 400°F (205°C) oven for 3–8 minutes, until the target temperature is reached.
Transfer to a plate and rest 5–10 minutes.
Optional: Slice and serve, spooning any pan juices over the top.