Season the venison all over with salt and pepper. Rub 1 teaspoon of the mustard evenly over each piece of meat. Now roll the meat around in the chopped parsley until both pieces of meat are evenly coated.
Lay 4 slices of prosciutto, shingled so that it creates a square shape on a piece of parchment paper. Place one piece of the venison in the center of the prosciutto square. Using the parchment paper to help you, roll the prosciutto tightly around the venison. Repeat this process for the other piece of meat. Refrigerate for at least 1 hour or up to overnight before cooking.
Heat a heavy bottomed pan over medium heat. Once hot, add the oil. Now add the venison with the prosciutto seam side down. Cook for about 2 minutes to form a seal on the prosciutto.
Cook the meat on all sides until the prosciutto has nicely browned, and/or until the venison is cooked to your desired internal temperature. If the prosciutto is crispy before you reach the internal temperature your'e looking for, you can finish them in a 225 degree F oven.
Let the meat rest for 5 to 10 minutes before slicing.