Cut the lettuces in half leaving the base of the stem intact to hold the leaves together. Brush the lettuces with the olive oil, well-seasoned with salt and pepper.
Then place cut side down on a preheated barbecue rack or one of those cast iron griddle pans with raised ridges. Cook for 3-5 minutes. They are ready when the outer leaves are well-charred, striped from the grill and the thick stems are just becoming tender.
Arrange the 12 lettuce halves in a dish and lay over thin slices of the cheese. Add a few more twists of pepper and a drizzle of leftover olive oil. Throw in a hot oven or under a grill until the cheese starts to bubble.
Serve at once. Two lettuce halves, smothered in bubbling cheese, per person.