Trim the beef sirloin steak and cut it into equally sized slices. Season both sides with salt and pepper.
Preheat a grill pan over medium-high heat and brush lightly with olive oil.
Place the beef slices in the hot grill pan and cook for 3-4 minutes on each side, depending on your desired level of doneness (3 minutes per side is sufficient for medium-rare).
After grilling, transfer the beef to a piece of aluminum foil and let it rest for 5 minutes, allowing the juices to redistribute evenly.
Meanwhile, prepare the mashed potatoes: peel and chop the potatoes, then place them in boiling salted water and cook until tender, about 15 minutes.
Drain the cooked potatoes, add the butter and warm milk, and mash until creamy. Season with salt to taste.
To serve, place the grilled beef on a plate alongside the mashed potatoes. Garnish with fresh, chopped parsley.
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