Divide the beef into 6 equal portions, 5 to 5.5 ounces each, and form into patties. Place the patties on a sheet pan and use your thumb to press a shallow dimple into the center of each one (this helps them hold their shape while grilling).
Preheat the grill (or grill pan) over medium-high heat, maintaining a temperature between 400℉ and 450℉.
Right before grilling, brush the tops of the patties evenly with Dijon mustard, then drizzle with olive oil and balsamic vinegar. Season both sides generously with salt and pepper.
When the grill is hot, add the burgers and cook until a golden-brown crust forms on each side and they reach desired doneness, 5 to 6 minutes per side for medium. Avoid pressing on the patties, as this forces out the juices, and flip only once for best results. During the last 1 to 2 minutes of cooking, top each patty with blue cheese crumbles, close the lid, and let the cheese melt just enough to adhere to the burgers. Transfer the patties to a clean plate and rest for 5 minutes to allow the juices to settle.