Bring the steaks to room temperature (20–30 minutes). Pat them very dry with paper towels and season generously on both sides with kosher salt and a few grinds of black pepper. Bringing steaks to room temperature ensures more even cooking; drying the surface and salting early helps the steaks form a better crust when seared.

Marinate quickly: in a small bowl combine 1/2 tbsp olive oil, the minced garlic, and the chopped rosemary leaves. Rub this mixture lightly over both steaks. Let sit while you prepare the vegetables. The oil carries the garlic and rosemary aromas onto the meat; because the contact time is short we won't overpower the steak but will still boost flavor.

Preheat the oven to 220°C (425°F). Line a large rimmed baking sheet with foil or parchment and arrange the cubed sweet potatoes in a single layer. Toss with 1 tbsp olive oil, 3/4 tsp kosher salt, 1/4 tsp black pepper, and a few torn rosemary leaves. Spread them so they have space — crowding causes steaming instead of browning. High oven heat and space on the pan create caramelization and crispy edges.

Start roasting the sweet potatoes in the preheated oven for 10 minutes. After 10 minutes add the broccoli: on the same sheet (if there's room) or a second sheet, toss the broccoli florets with the remaining 1/2 tbsp olive oil, a pinch of salt and pepper, and spread in a single layer. Return both sheets to the oven. Staggering the vegetables keeps smaller florets from overcooking and lets the sweet potatoes get a head start so everything finishes together.

Roast vegetables for another 15–20 minutes, tossing once halfway through, until the sweet potato cubes are tender with deeply browned edges and the broccoli has crisp-tender stems and charred tips. About 25–30 minutes total for the potatoes and 15–20 minutes for the broccoli is typical. Add the remaining minced garlic over the vegetables for the final 6–8 minutes — this prevents the garlic from burning and gives a fresher roasted garlic flavor.

While vegetables roast, preheat a heavy cast-iron skillet or grill pan over high heat until very hot (3–5 minutes). A screaming-hot pan is essential to get an immediate sear — the Maillard reaction creates the flavorful brown crust that distinguishes restaurant-quality steak.

Just before cooking, brush or pat any excess garlic from the steaks (you want the surface dry to sear). Place the steaks into the hot, dry skillet. For 2 cm–2.5 cm (about 3/4–1") thick sirloins: cook 3½–4½ minutes per side for medium-rare (internal temperature 53–57°C / 127–135°F), 5–6 minutes per side for medium. Resist moving the steaks once you place them — uninterrupted contact forms the crust. Tip: use tongs and lift the steak after 3 minutes to check for a deep brown crust before flipping.

If you like, add a sprig of rosemary to the pan during the last minute and spoon any rendered juices over the steaks. This quick baste adds aroma and a glossy finish. Avoid adding butter earlier — it will brown and burn at very high searing temperatures; add it only in the last 30 seconds if you prefer a buttery finish.

Transfer the steaks to a cutting board and tent loosely with foil. Rest for 6–8 minutes. Resting allows the juices to redistribute inside the meat; cutting too soon will lose those juices on the cutting board and dry the steak.

While steaks rest, finish the vegetables: if any potatoes need extra browning, return them to the oven for 2–4 minutes under the broiler (watch carefully). Sprinkle the roasted vegetables with a small pinch of flaky sea salt and a little lemon zest or a squeeze of lemon to brighten the dish.

Slice the steaks against the grain into 5–7 mm slices and arrange on warmed plates. Spoon the roasted sweet potatoes and broccoli alongside. Garnish with a few fresh rosemary needles and lemon wedges. Slicing against the grain shortens the muscle fibers and makes each bite more tender.

Serve immediately with any pan juices drizzled over the steak. Enjoy the contrast of the savory, herb-forward steak and the sweet, caramelized potatoes with the smoky bite of the broccoli.