Preheat your grill or a heavy cast-iron grill pan over medium-high heat.
Prick the eggplant several times with a fork and place it directly on the grill grates, turning occasionally until the skin is charred and the flesh is completely soft, about 15-20 minutes.
Remove the eggplant from the heat, let it cool slightly, then slice open and scoop the soft flesh into a bowl, discarding the charred skin.
Mash the eggplant flesh with a fork or pulse in a food processor with the tahini, lemon juice, minced garlic, cumin, and half of the sea salt until creamy.
Brush the top sirloin steak with half of the olive oil and season both sides with the remaining sea salt and black pepper.
Grill the steak for 4-5 minutes per side for medium-rare, or until it reaches your preferred level of doneness.
Remove the steak from the grill and let it rest on a cutting board for 5 minutes to lock in the juices.
Spread the baba ghanoush onto a plate, slice the steak against the grain, and lay the strips over the eggplant puree.
Drizzle with the remaining olive oil and garnish with freshly chopped parsley before serving.