Cut the courgette diagonally into 1/4-inch-thick slices so they are the size of the the width of the bread. Spread them out on a plate or cutting board and season both sides with salt and pepper.
Preheat a griddle or grill pan to medium-high.
Cut the bread into 6-inch segments and then cut each segment horizontally almost completely through so you can open it like a book. Open the sandwich halves and press them flat against the work surface with your hands until the bread doesn't spring back. Put cheese on the bottom half of each sandwich.
Working in batches, melt 1 tablespoon butter on the griddle. Cook the courgette until slightly browned and soft, about 3 minutes. Turn and cook until pliable and nearly transparent, another 2 minutes. As courgette is cooked, put it on top of the cheese, dividing equally among the sandwiches. Divide the olives among the sandwiches and close them, pressing to flatten.
Working in batches, reduce the heat to medium-low and melt 1 tablespoon butter (for a small griddle) or 2 tablespoons butter (for a large griddle). Put the sandwiches on the griddle. Place a baking sheet on top of the sandwiches and weigh it down with something heavy, like canned goods or a cast-iron skillet. The idea is to make the sandwiches as flat as possible. (Alternatively, use a panini press.)
Cook until the bread is crisp, about 3 minutes. Turn and cook, adding more butter if necessary, until the cheese is melted and the bread is crisp, 2 minutes more. Serve immediately.
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