In a small saucepan over medium heat, add the blueberries, balsamic, and honey. Stir to mix well. Cook, gently stirring the blueberries and lightly mashing them, until they soften and turn almost jammy, about 5 minutes. Set aside.
Butter the outside of each slice of bread. On the unbuttered side of one slice of bread, spoon a layer of the blueberry mixture, add basil, and about 2-3 slices of brie, or desired amount. Top with the remaining slice of bread, buttered side up. Repeat for next sandwich.
In a skillet or grill pan over medium heat, add the sandwiches (or make one at a time) browning each side until golden brown and the cheese is melted.