Tie the eye of round roast at 1.5-inch intervals with kitchen twine to create an even cylinder for uniform cooking.
In a small bowl, mix the kosher salt, black pepper, garlic powder, dried thyme, and dried rosemary with the olive oil to form a paste, crushing the rosemary between your fingers as you add it.
Rub the paste all over the roast, set it on a rack over a tray, and refrigerate uncovered for 6–24 hours.
Remove the roast from the refrigerator 45 minutes before cooking. Pat it dry. Preheat the oven to 225°F and set a rack in the middle position.
Heat the vegetable oil in a heavy skillet over medium-high heat until shimmering. Sear the roast on all sides until well browned, 2–3 minutes per side (about 8–10 minutes total).
Transfer the roast to a rack set in a roasting pan. Insert a probe or instant-read thermometer into the center. Roast at 225°F until the internal temperature reaches 120–125°F for medium-rare, 60–90 minutes (20–30 minutes per pound); the exterior will be browned and the center will feel very springy.
Move the roast to a cutting board, tent loosely with foil, and rest 20–30 minutes to allow juices to redistribute.
Place the hot skillet (or roasting pan) over medium heat, pour in the low-sodium beef broth, and scrape up the browned bits. Simmer until reduced by about one-quarter, 5–7 minutes; keep warm.
Remove twine. Slice the roast very thinly across the grain with a sharp knife. Serve with the warm pan juices.