Pat the steak dry with paper towels and season generously on all sides with salt, pepper, and paprika (if using). Cut the potatoes into even halves or quarters so they cook uniformly.

Heat 2 tablespoons of olive oil in a large skillet over medium-high heat. Add the potatoes in a single layer and cook, stirring occasionally, until golden brown and tender, about 12-15 minutes. Season with salt and pepper, then transfer to a plate.

In the same skillet, add the remaining 1 tablespoon olive oil over high heat. Place the steak in the pan and cook without moving for 4-5 minutes per side for medium-rare, or until desired doneness. Add the butter and minced garlic during the last minute, tilting the pan and spooning the melted butter over the steak.

Remove the steak from the skillet and let it rest on a cutting board for 5 minutes. Then slice against the grain into thin strips.

Return the cooked potatoes to the skillet with the garlic butter. Toss to coat and heat through. Add the sliced steak and any accumulated juices, then sprinkle with fresh parsley. Serve immediately on a white plate.