Preheat the oven to 450°F (230°C). Set a rack in the center and line a small roasting pan with foil. Pat the beef dry and rub all over with the olive oil.
Season the roast on all sides with 2 tsp kosher salt, 1.5 tsp black pepper, the garlic powder, and dried thyme.
Roast at 450°F for 15 minutes. Reduce the oven to 325°F (165°C) and continue roasting 25–40 minutes, until the internal temperature reaches 125°F for medium-rare (the center should feel springy and a thermometer should read 125°F).
Transfer the roast to a cutting board, tent loosely with foil, and rest 20 minutes, then chill 20–30 minutes for cleaner slicing.
While the beef rests, make the horseradish sauce: In a bowl, whisk together the mayonnaise, sour cream, prepared horseradish, Dijon mustard, lemon juice, and the remaining 0.25 tsp kosher salt and 0.25 tsp black pepper. Set aside.
Prepare the sandwich fixings: Rinse and pat dry the romaine leaves, then shred them. Slice the tomato and red onion into 8 slices each if not already sliced. Split the sandwich rolls.
Thinly slice the rested beef against the grain.
Toast the rolls: Melt the butter in a large skillet over medium heat. Place the rolls cut-side down and toast until golden, 1–2 minutes.
Assemble each sandwich: Spread horseradish sauce on both cut sides of a roll (about 2–3 tbsp total). Pile about 4 oz sliced beef on the bottom half. Add shredded romaine, 2 tomato slices, 2 red onion slices, and 2 dill pickle slices. Cap with the top roll, press gently, and serve immediately.