Preheat your oven to 400°F and line a large baking sheet with parchment paper for easy cleanup.
Peel and dice the sweet potato into 1/2-inch cubes, then toss them on the baking sheet with half of the olive oil and a pinch of salt and pepper.
Roast the sweet potatoes for 10 minutes, then add the broccoli florets to the same tray, tossing with the remaining oil and roasting for an additional 15 minutes until the vegetables are tender and slightly charred.
While the vegetables roast, pat the steak dry with paper towels and season both sides generously with the remaining salt and pepper.
Heat a cast-iron skillet over medium-high heat until very hot, then sear the steak for 3 to 4 minutes per side for a perfect medium-rare finish.
In the final minute of searing, add the smashed garlic clove and the rosemary sprig to the pan, tilting the skillet to spoon the infused juices over the steak.
Transfer the steak to a cutting board and let it rest for at least 5 minutes to lock in the juices before slicing it thinly against the grain.
Plate the sliced steak alongside the roasted sweet potatoes and broccoli, drizzling any remaining pan juices over the meat.