Preheat a 12-inch stainless steel skillet over medium heat, and add the oil.
1 tablespoon neutral oil
Season the steak lightly with salt. Once the oil barely begins to shimmer, add the steak.
1 filet mignon, kosher salt
Cook for two to three minutes, moving the steak to a different part of the pan each minute.
Flip the steak and cook for another two to three minutes, moving the steak to a hotter portion of the pan after one minute. Add the butter, rosemary, garlic (cut side down), sage, and thyme.
½ stick salted butter, 2 large rosemary sprig, 1 garlic head, 2 large sage sprig, 6 thyme sprig
Continuously baste the steak for another two minutes, or until the internal temperature reaches 120°F (49°C) or the desired internal temperature. (See chart below.) If the butter begins to darken too quickly, remove the pan from the heat, and baste continuously while the pan cools slightly. Then, return the pan to the heat as you notice the butter cooling. Repeat this process as needed.
Remove the pan from the heat and transfer the steak to a cutting board. Let the steak rest for five to ten minutes.
Transfer to a serving platter, top with a slice of compound butter, and serve warm.