To make the gremolata, combine the parsley, garlic and lemon rind in a small bowl, and season with salt and pepper.
Preheat grill on high. Place half the mushrooms, stem-side up, on a baking tray. Cook under preheated grill, about 6 cm from the heat source, for 5-6 minutes or until juices start collecting in the caps. Turn and cook for 2-3 minutes or until tender. Transfer to a serving plate.
Sprinkle mushrooms with gremolata and drizzle with olive oil. Serve immediately.