Combine butter, parsley, chile flakes, garlic, lemon zest, salt, and pepper in a bowl; set aside. Using a cleaver, split lobster in half lengthwise through its head and tail. Scoop out and discard the yel- low-green tomalley and break off claws. Transfer lobster halves, shell side down, to a baking sheet; crack claws and place them on the baking sheet. Drizzle halves and claws with oil, and season with salt and pepper.

Heat a charcoal grill or set a gas grill to high. Place lobster halves, flesh side down, and claws on hottest part of grill; cook until slightly charred, 2-3 minutes. Flip lobster over and using a spoon, spread lobster with the garlic parsley butter; continue grilling until lobster meat is tender, 3-5 minutes more.