Preheat the barbecue.
Cut the stem out of the mushrooms, then score with a knife over the grills, not cutting through to the other side.
Choose pairs of equal size. Lay one of each pair grill-side up on a work surface, then season to taste with salt and black pepper.
Add one tablespoon vermouth or white wine, followed by a little garlic and thyme, and finishing with grated cheese.
Place another mushroom on top and drive a cocktail stick or skewer through from the top to secure together.
Brush all over with olive oil.
Cook over hot coals, turning frequently and carefully, until very soft, juicy, and melting inside.
Serve with crusty bread.