Form ground beef in four equal patties (6-ounces each); refrigerate.
In a small sauce pan bring balsamic vinegar to a boil over medium-high heat. Add brown sugar, stir until dissolved. Reduce heat to low and simmer 10 - 15 minutes until vinegar is reduced by half; remove from heat. Note: Keep the flame low. Simmering on high heat can cause bitterness.
While 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 burgers 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.
Place the greens on the bottom of four buns, drizzle with balsamic reduction, top with burger and top bun.