Preheat the oven to 350 degrees F (175 degrees C).

Combine 2 tablespoons olive oil, garlic, thyme, rosemary, 1 teaspoon salt, and black pepper in a small bowl; set aside.

Heat 1 tablespoon olive oil in a large oven-proof skillet over medium-high heat. Add tenderloin; cook until well-browned, 2 to 3 minutes. Flip tenderloin; turn off heat. Spread garlic-herb oil evenly over top and sides of tenderloin.

Cook in the preheated oven until an instant-read thermometer inserted into the center reads 125 degrees F (50 degrees C), 25 to 30 minutes. Transfer tenderloin to a carving board; tent with foil and let stand 10 minutes. (Internal temperature will rise to 130 degrees F (54 degrees C) for medium-rare.)

Meanwhile, combine sour cream, horseradish, remaining 1 tablespoon oil, and remaining 1/2 teaspoon salt in a small bowl; chill until ready to serve.

Carve tenderloin crosswise into 1/2-inch thick slices; serve with horseradish sauce.