Peel and mince the garlic. In a small bowl whisk together olive oil, soy sauce, Worcestershire sauce, minced garlic, black pepper, kosher salt, and smoked paprika until combined.

Trim and score

Pat the bottom sirloin dry with paper towels. If the roast has a thick fat cap, trim to about 1/4 inch. Lightly score the fat in a crisscross pattern (if present) to help flavors penetrate.

Marinate

Place the meat in a shallow dish or zip-top bag. Pour the marinade over the sirloin, rubbing it so all surfaces are coated. Add the rosemary sprigs. Refrigerate for at least 1 hour or up to overnight (for best flavor, 4–12 hours). Remove from fridge 30 minutes before cooking to come toward room temperature.

Cook & Finish

Preheat and sear

Preheat oven to 375°F (190°C). Heat a heavy oven-safe skillet (cast iron preferred) over high heat until very hot. Add 1 tablespoon olive oil. Remove the sirloin from the marinade (reserve marinade) and pat lightly dry. Sear the meat, fat-side down first if present, 2–3 minutes per side until a deep brown crust forms. Use tongs to hold on edges and sear any unbrowned sides (about 30–60 seconds per edge).

Deglaze and roast

Reduce heat to medium. Pour the reserved marinade into the pan and let it sizzle 30 seconds to deglaze, scraping up browned bits. Add beef broth to the pan. Transfer the skillet to the preheated oven and roast uncovered. For a 2 lb sirloin roast, roast 20–30 minutes for medium-rare (internal temp 125–130°F / 52–54°C), 30–35 minutes for medium (135°F / 57°C). Use an instant-read thermometer inserted into the thickest part to check doneness.

Rest and finish sauce

Remove the skillet from oven and transfer the sirloin to a cutting board. Tent loosely with foil and rest 10–15 minutes (temperature will rise ~5–10°F). While meat rests, place the skillet back on medium heat. Add butter and lemon zest and juice, stirring to melt and incorporate with pan juices. Simmer 1–2 minutes until reduced slightly. Taste and adjust with a pinch of salt or a splash of broth if needed.

Slice and serve

Slice the bottom sirloin thinly across the grain into 1/8–1/4 inch slices. Arrange on a platter, spoon the pan sauce over the slices, and garnish with the rosemary sprigs. Serve immediately.