Heat 1 tablespoon of olive oil and 1 tablespoon butter over medium heat. Add onions, season with salt and pepper and cook until caramelized and sweet, about 20 minutes. Stir sugar and water into onions then add mustard, combine and turn off heat.
Combine meat with garlic, Worcestershire, parsley, salt and pepper, form 4 patties thinner at the center and thicker at the edges for even cooking. Also, the burgers will bulge as they cook, this will give the cooked burgers an even thickness. Cook patties 8 minutes turning once for medium doneness, 1 to 2 minutes less for rare patties, 1 to 2 minutes more for burgers that are medium well. In the last minute of cooking time, top burgers with a few slices of Cambozola blue.
Place burgers on bun bottoms and top with some arugula and mustard glazed onions, set tops in place.