Preheat the oven to 200 degrees Celsius. Cut the sweet potato into even cubes. Spread the cubes over a baking sheet, season with salt and pepper, and roast for twenty minutes until tender. Meanwhile, cut the broccoli into florets and peel and mince the garlic cloves.
Bring a pot of water to a boil and blanch the broccoli for four minutes until tender-crisp. Drain the vegetable and let it drain well. Pat the steak dry and season both sides with salt and pepper. Heat half the butter in a skillet over high heat and cook the steak with the rosemary for three minutes per side.
Remove the steak from the pan, tent loosely with foil, and let the meat rest for five minutes on a cutting board. Lower the heat slightly and melt the remaining butter in the warm skillet. Add the minced garlic and drained broccoli and sauté for a few minutes until the flavors are well combined.
Slice the rested steak. Divide the roasted sweet potato and warm garlic broccoli among the plates. Add the sliced steak alongside and serve immediately.