Massage the oil and garlic into the beef and evenly coat with the herbs, salt and black pepper. Cover with plastic wrap and let it sit at room temperature for 1 hour.
Place celery, onion, carrot and bay leaves in 4-inch half hotel pan. Place the seasoned beef on top of the bay leaves. Roast at 400°F for 45 minutes to create a nice sear on the outside. Reduce temperature to 185°F and roast 1 hour longer or until the internal temperature reaches 120°F. Remove pan from the oven; let the beef rest at room temperature for 30 minutes.
Trim the fat off the beef and leave in the roasting pan. Reserve fat, vegetables and pan drippings. Refrigerate the beef, uncovered, for 2 hours to cool completely. Thinly shave the beef across the grain.
For the au jus:
Add broth to the pan with reserved fat, vegetables and pan drippings. Heat to a boil over high heat, scraping bottom of pan to remove the fond. Reduce heat to low and simmer for 30 minutes. Drain the au jus through a fine sieve and reserve.
For the caramelized onions:
Melt the butter in a medium sauté pan over medium high heat. Add the onions, salt and white pepper and cook 20 minutes or until the onions are translucent and caramel colored, stirring occasionally.
For the horseradish sauce:
Stir together the mayonnaise, sour cream and horseradish in a bowl. Cover and refrigerate up to 5 days.
Open hoagie roll flat and butter the inside. Toast buttered side down on a medium-high griddle or sauté pan. Spread toasted side with horseradish sauce.
Heat au jus in a medium saucepot to a simmer. Add 6 ounces shaved beef to the hot au jus and heat through. Place beef and ¼ cup onions in toasted hoagie roll and serve with 4 ounces au jus in a small bowl for dipping.