Take the beef tenderloin out of the refrigerator and set it on the counter so it can lose its chill and come to room temperature; this usually takes about 1 to 2 hours. Allowing the meat to warm slightly helps it cook more evenly from edge to center.
In a small mixing bowl, combine the softened butter, minced garlic, chopped rosemary, and chopped thyme. Stir until you have a smooth, fragrant garlic herb butter. Set this aside; it will be used to coat the roast before it goes into the oven.
Preheat your oven to 425°F (220°C). If your beef tenderloin has not already been trimmed and tied by the butcher, slice it in half for easier handling, trim any excess silver skin or uneven ends, and tie it at intervals with kitchen twine so it holds a uniform shape as it roasts.
Using paper towels, thoroughly pat the beef tenderloin dry on all sides to remove any surface moisture, which helps the meat sear instead of steam. Season the entire roast generously with kosher salt and freshly ground black pepper, pressing the seasoning lightly into the surface so it adheres.
Place a large cast-iron pan over medium-high heat and add the avocado oil. When the oil is hot and shimmering, carefully lay the beef tenderloin in the pan. Sear it for several minutes on each side, turning as needed, until a deep golden brown crust forms all around—this should take about 10 minutes in total.
Once the meat is well-browned, turn off the heat. Spread the garlic herb butter mixture generously over the top of the tenderloin, letting some of it melt and run down the sides. If you’re using a probe thermometer, insert it into the thickest part of the roast at this stage. Transfer the entire pan to the preheated oven and roast for 15 to 20 minutes, or until the internal temperature reaches your preferred doneness.
Remove the pan from the oven and carefully transfer the beef tenderloin to a cutting board. Let the roast rest, untouched, for 10 to 15 minutes so the juices can redistribute throughout the meat and the internal temperature can stabilize. After resting, cut away the kitchen twine and slice the tenderloin into 1-inch thick medallions. Serve immediately, with horseradish sauce on the side if you’d like an extra punchy accompaniment.