Heat a frying pan over a high heat. When the pan is smoking, add the pancetta and dry-fry for 1-2 minutes on each side, or until crisp and cooked through. Drizzle over the maple syrup and transfer the pancetta to a warm plate.
Lay four slices of the brioche onto a chopping board and top each with a slice of Gruyère and three slices of the pancetta. Drizzle over the pan juices, then top with the remaining slices of brioche.
Whisk the eggs, sugar and milk in a shallow, wide bowl until well combined, then season, to taste, with salt and freshly ground black pepper.
Dip each sandwich into the egg mixture, allowing the brioche slices to soak for a few seconds on each side.
Heat half of the butter in a large frying pan over a medium heat. When the butter is foaming, add two of the soaked sandwiches and fry gently for 4-5 minutes on each side, or until golden-brown on both sides and heated through. Keep warm. Repeat the process with the remaining butter and the remaining two sandwiches. Serve immediately.