In a small saucepan over medium heat, combine the blackberries, balsamic vinegar, and honey.
Cook for 5-7 minutes, stirring occasionally, until the mixture thickens slightly. Remove from heat.
Butter one side of each slice of bread.
Place two slices of bread, buttered side down, on a skillet over medium heat.
Layer with mozzarella cheese, crumbled goat cheese, and a spoonful of the balsamic blackberry mixture.
Sprinkle with salt, black pepper, and thyme if using.
Top with the remaining bread slices, buttered side up.
Grill for 3-4 minutes per side, until golden brown and the cheese is melted.
Remove from heat, slice in half, and serve warm.