Form ground beef in four equal patties (170 grams each); refrigerate.
In a small sauce pan bring balsamic vinegar to a boil over medium-high heat. Add brown sugar, and stir until dissolved. Reduce heat to medium-low and simmer 10 minutes until vinegar is reduced by half; remove from heat.
While the sauce reduces, crisp prosciutto in a cast iron skillet over medium-high heat for about 5 minutes; remove from skillet and reserve for topping.
Season patties with salt and pepper. In the same cast iron skillet, cook burgers over medium-high heat on the first side for 3-4 minutes. Flip burgers and top each with blue cheese and prosciutto. Cover and cook another 3-4 minutes or until burgers reach an internal temperature of 160°F (71°C).
Place arugula on the bottom of four buns, drizzle with balsamic reduction, and top with burger and top bun.
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