Start by preheating the oven to 375 degrees. Lay your prosciutto pieces on a aluminum lined pan so that they are not touching. Cook for 13-15 minutes until crsipy.
While the prosciutto is cooking form the ground turkey into 4 patties. Generously season both sides heavily with salt and pepper.
In a cast iron pan preheated over high heat—add a splash of olive oil, place the patties in the pan and reduce the heat to medium. Cook for 7 minutes, flip and cook the other side for another 7 minutes. Pull when the patties reach an internal temperature of 165 degrees.
After you pull the patties, turn the heat back up to high. Brush the cut side of your hamburger buns with melted butter and toast in the pan until brown.
Create the rosemary aioli for the burger by mincing the rosemary and mixing it together with the mayo.
Time to build the burger! Start by slathering the bottom bun with 1 1/2 teaspoon of the rosemary aioli. Next add 2 slices of prosciutto and top with the burger patty. Lay a slice of brie on top and sprinkle over 1 teaspoon of sugar. Using a brulee torch caramelize the sugar. Top with 1/4 cup of arugula and finish it off with the top bun smothered with another 1 1/2 teaspoon of rosemary aioli.