01 - In a small saucepan over medium heat, combine balsamic vinegar and honey. Simmer gently for 3 to 5 minutes, stirring, until the mixture thickens into a glaze. Remove from heat and allow to cool slightly.
02 - Spread softened butter on one side of each slice of sourdough bread.
03 - Arrange two slices of bread, buttered side down, on a clean work surface. Evenly layer sliced brie over each, then top with shredded sharp white cheddar and halved blackberries. Drizzle each sandwich interior with one teaspoon of prepared balsamic glaze.
04 - Place remaining bread slices on top of each, buttered side facing outwards, to complete the sandwiches.
05 - Preheat a nonstick skillet or griddle over medium heat. Add assembled sandwiches and cook for 3 to 4 minutes per side, pressing gently, until the exterior is golden brown and the cheeses are melted.
06 - Remove sandwiches from heat and allow to rest for one minute. Slice carefully and serve while warm.