In a skillet, cook the bacon over medium heat until crispy, about 6-8 minutes. Once cooked, transfer to a paper towel-lined plate to drain excess fat. Reserve some bacon grease in the skillet for grilling the sandwiches for added flavor.
While the bacon is cooking, rinse the blackberries gently and set them aside.
Butter one side of each slice of bread. Make sure to cover the entire surface for even toasting.
On the unbuttered side of four slices of bread, layer the following: a slice of cheese, 2 slices of cooked bacon, a few blackberries, and another slice of cheese. Season lightly with salt and pepper.
Top with the remaining slices of bread, making sure the buttered side is facing out.
Heat the skillet over medium heat. Working in batches if necessary, place the sandwiches in the hot skillet. Cook until the bottom is golden brown and the cheese begins to melt, about 3-4 minutes.
Carefully flip the sandwiches, using a spatula, and continue to cook until the second side is golden brown and the cheese is fully melted, around another 3-4 minutes.
Remove the sandwiches from the skillet, let them cool for a minute, and then cut them in half diagonally. Serve warm.