Pat the trimmed tenderloin completely dry with paper towels, then coat every surface generously with coarse kosher salt. Place uncovered on a wire rack set over a sheet pan and refrigerate for 8–24 hours until the surface looks dry and tacky.
Remove the tenderloin from the refrigerator 45–60 minutes before smoking. Fold the thin tail end underneath the roast and tie with butcher's twine at 1.5–2 inch (4–5 cm) intervals to create an even cylinder from end to end.
Combine black pepper, garlic powder, onion powder, smoked paprika, dried rosemary, and dried thyme in a small bowl. Coat the tenderloin evenly with olive oil, then press the dry rub firmly onto all surfaces including the ends.
Preheat your smoker to 250°F (121°C) using oak or hickory wood and allow it to fully stabilize before adding the meat. Set up for indirect heat if using a charcoal grill.
Place the trussed tenderloin on the grill grate over indirect heat and insert a leave-in probe into the thickest part if available. Smoke undisturbed at 250°F (121°C) until the internal temperature reaches 110°F (43°C), approximately 60–75 minutes total.
Remove the tenderloin from the smoker at 110°F (43°C) and tent loosely with aluminum foil. Rest for 10 minutes while you heat your grill or cast iron skillet to its highest possible temperature (500°F / 260°C or higher).
Sear the tenderloin for 2–3 minutes per side on all four surfaces until a deep mahogany crust forms, monitoring closely with an instant-read thermometer. Pull from the heat when the internal temperature reaches 125°F (52°C) for medium-rare or 130°F (54°C) for medium.
Transfer the seared tenderloin to a clean cutting board, tent loosely with foil, and rest for 10–15 minutes. Carryover cooking will raise the internal temperature an additional 3–5°F (1–3°C) during this time.
While the tenderloin rests, stir together sour cream, prepared horseradish, fresh lemon juice, and Dijon mustard in a small bowl. Season with salt and pepper to taste, then refrigerate until ready to serve.
Remove the butcher's twine, then slice the tenderloin into 1–1.5 inch (2.5–4 cm) medallions using smooth, even strokes with a sharp carving knife. Arrange on a serving platter, drizzle with resting juices, and serve immediately with the horseradish cream sauce on the side.