01 - In a small saucepan over medium heat, combine balsamic vinegar and honey. Simmer for 3 to 5 minutes, stirring occasionally, until the mixture thickens. Remove from heat and allow to cool slightly.
02 - Spread softened butter evenly across one side of each slice of sourdough bread.
03 - Place two bread slices, buttered side down, on a clean work surface.
04 - Layer equal portions of brie slices onto the bread, followed by shredded sharp white cheddar and blackberry halves. Drizzle with 1 teaspoon of balsamic glaze per sandwich.
05 - Top with remaining bread slices, buttered side facing up.
06 - Preheat a nonstick skillet or griddle over medium heat. Carefully transfer sandwiches into the skillet. Cook for 3 to 4 minutes on each side, pressing gently, until bread is golden brown and cheese has melted.
07 - Remove sandwiches from heat. Let rest for 1 minute, then slice and serve warm.