Preheat a skillet or griddle over medium heat.
Spread softened butter on one side of each slice of bread.
On the unbuttered side of 4 slices, layer the shredded cheddar cheese evenly.
Scatter fresh blackberries over the cheese, then drizzle balsamic glaze on top.
Season with salt and pepper to taste.
Top with the remaining 4 slices of bread, buttered side facing out.
Place the sandwiches in the preheated skillet and cook for about 3-4 minutes on each side, or until the bread is golden brown and the cheese is melted.
Remove from the skillet, let cool for a minute, then slice in half and serve warm.