Divide the beef into 6 loosely packed 1/2-inch-thick patties about 4 1/2 inches in diameter. Set aside.
Combine the blueberries, sugar, lemon juice and a pinch of salt in a medium saucepan. Bring to a boil over high heat. In the meantime, stir together the cornstarch and water in a medium bowl. When the blueberry mixture comes to a boil, slowly drizzle in the cornstarch slurry and cook until the blueberry mixture slightly thickens to the consistency of pancake syrup. Set aside to cool to room temperature.
Place the coarse pepper on a rimmed baking sheet. Sprinkle the burger patties liberally with salt and place one by one in the coarse pepper to coat generously, pushing firmly on each side.
Cook the burgers in a hot cast-iron pan with a little oil to get them started. Cook 4 minutes on one side, and then flip and cook 3 minutes on the other side to medium-rare. Remove to a warm plate covered with foil to rest while cooking the remaining burgers.
Meanwhile, cut and toast the buns cut-side down in a separate pan with a touch of oil for extra crunch. Spread the toasted buns liberally with the basil aioli. Place a burger on the bottom bun, followed by some blue cheese, a few spoonfuls of blueberry sauce, 2 slices bacon, a slice of red onion and a big pinch of arugula. Repeat with the remaining burgers.
Blend the basil, lemon juice, garlic and oil to make a smooth puree in a blender. Mix it with your favorite mayonnaise (2 parts mayonnaise to 1 part basil puree).
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.