Rub the beef tenderloin all over with kosher salt. Tie up with kitchen twine. Refrigerate uncovered overnight.
Preheat the oven to 450ºF.
Use a kitchen towel to blot away any excess moisture from the outside of the tenderloin. Season with cracked black pepper.
In a small bowl, mix together the butter, horseradish, and garlic.
Melt 1 tablespoon of the butter mixture in a large cast-iron skillet and heat over medium-high heat. Add the fresh herbs.
Sear the beef tenderloin on all sides, about 1 to 2 minutes per side, creating a brown caramelized crust. Spoon the hot butter over the tenderloin as it sears.
Spread the seared tenderloin with the remaining butter mixture. Transfer the pan to the oven and roast until an instant read thermometer registers your desired temperature, about 20 to 30 minutes. (See suggested temperatures above.)
Remove the tenderloin from the oven and transfer to a cutting board. Let rest for 15 to 20 minutes to allow the juices to redistribute before slicing into ¾ inch slices.
Serve warm, with au jus or horseradish cream sauce.