In a medium bowl mix the blue cheese, mayonnaise, vinegar and ½ teaspoon of pepper to make a dressing. Add the coleslaw blend and toss in the dressing. Cover and refrigerate until ready to use.
In a large skillet over medium heat, fry the bacon until crisp, about 10 minutes, turning occasionally. Drain the bacon on a plate lined with a paper towel.
Prepare the grill for direct cooking over medium–high heat (200ºC to 260ºC).
Mix the ground chuck, salt and ¾ teaspoon of pepper. Gently form four patties of equal size, each about 2 centimetres thick. With your thumb or the back of a spoon, make a shallow indentation about 2.5 centimetres wide in the centre of each patty to prevent them from doming as they cook. Refrigerate the patties until ready to grill.
Brush the cooking grates clean. Grill the patties over direct medium–high heat, with the lid closed, until cooked to medium doneness, 9 to 11 minutes, turning once. During the last 30 seconds to 1 minute of grilling time, place a slice of cheddar cheese on each patty to melt and toast the buns, cut-side down, over direct heat.
Build each burger on a bun with a patty, a strip of bacon (torn in half), an onion slice and the coleslaw. Serve warm.