01 - Combine balsamic vinegar and honey in a small saucepan over medium heat. Simmer for 3 to 5 minutes, stirring occasionally, until mixture thickens. Remove from heat and let cool slightly.
02 - Spread softened butter on one side of each bread slice. Arrange two slices, buttered side down, on a clean surface.
03 - Distribute sliced brie evenly over the bread, then sprinkle with shredded cheddar and scatter halved blackberries over the cheese. Drizzle each with approximately 1 teaspoon of balsamic glaze.
04 - Place the remaining bread slices, buttered side up, over the fillings to form sandwiches.
05 - Heat a nonstick skillet or griddle over medium heat. Grill the sandwiches for 3 to 4 minutes per side, gently pressing, until golden brown and the cheese is melted.
06 - Remove sandwiches from the pan and rest for 1 minute. Slice as desired and serve immediately while warm.