Preheat grill or broiler oven. Snap off woody ends of each asparagus stalk and place asparagus into a large ziptop bag. Add in oil, vinegar and some salt and pepper. Seal bag and shake contents to coat asparagus well. Slice camembert and top bread slices with it.
Place asparagus and cheese bread onto the grill. Grill asparagus about 4 minutes per side and toast bread until crisp and cheese has melted. Transfer bread onto a cutting board and top with five or six asparagus spears. With a large knife, cut bread into three or four smaller pieces and transfer to a serving platter.
Drizzle bread with more balsamic vinegar. Serve immediately.