Place a medium sized pot over medium-low heat. Add the butter and melt. Now add the flour, stir to combine and cook for two minutes. Stir frequently to prevent burning the roux.
Slowly add in the chicken stock while whisking to combine thoroughly. Add the remaining ingredients and cook at a slow simmer until it is thick enough to coat the back of a spoon. Season with salt and pepper to your liking.
For the Venison
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.
Nutrition information is automatically calculated, so should only be used as an approximation. Nutrition is per serving.