1. Start by making the blueberry mixture. In a small saucepan over medium heat, combine the blueberries, honey, and balsamic vinegar. Stir occasionally until the blueberries begin to burst and the mixture thickens, about 5-7 minutes. Season with a pinch of salt and pepper, then set aside.
2. Lay out the sourdough slices on a flat surface. Spread butter on one side of each slice. This will be the side that grills to a golden perfection.
3. On the unbuttered side, layer slices of Brie and sharp cheddar cheese. Add a generous spoonful of the blueberry mixture over the cheese.
4. Top with another slice of bread, buttered side facing out.
5. Preheat a skillet over medium heat. Place the sandwiches in the skillet and cook until the bread is golden brown and the cheese has melted, about 3-4 minutes per side. Keep an eye on them, as they can brown quickly.
6. Remove from the skillet, let them cool for a minute, then slice and serve.

Remember, the secret to a perfect grilled cheese is a low and slow approach. This allows the cheese to melt thoroughly while achieving that perfect crispy crust.