01 - In a small saucepan over medium heat, combine balsamic vinegar and honey. Simmer gently for 3 to 5 minutes, stirring occasionally, until the mixture thickens. Remove from heat and allow to cool slightly.
02 - Spread softened butter on one side of each piece of sourdough bread. Arrange two slices, buttered side down, on a clean surface.
03 - Layer brie slices evenly across the bread. Sprinkle with shredded sharp white cheddar and distribute blackberry halves. Drizzle 1 teaspoon of prepared balsamic glaze over each.
04 - Cover each assembled slice with remaining bread, buttered side facing outward.
05 - Heat a nonstick skillet or griddle over medium heat. Place assembled sandwiches on the pan and cook 3 to 4 minutes per side, pressing gently, until bread is golden and cheese has melted.
06 - Transfer sandwiches to a board, let rest 1 minute. Slice and serve while warm.