Whisk together the balsamic vinegar, brown sugar, salt and pepper. I like to dissolve the sugar before I add the olive oil.
Whisk in the olive oil. This can be made a few days ahead of time and kept in the fridge.
Quarter the peppers. Spray them with cooking spray.
Grill the peppers on a preheated medium high grill. Cook about 5 minutes on each side with the lid closed.
Drizzle with the dressing. Add crumbled blue cheese and torn basil leaves.
Season with salt and pepper.