Preheat the oven to 400°F.
Heat a skillet over medium heat and add 1 tablespoon butter. Add the shallots, minced garlic, and mushrooms. Cook, stirring occasionally, for 4–5 minutes until the mushrooms are softened and lightly golden. Stir in the parsley, then remove from heat and allow the mixture to cool slightly.
Place the elk tenderloin on a cutting board and carefully butterfly it open using a sharp knife. Using a meat mallet, gently pound the tenderloin to an even thickness of about ½ inch. Season generously with kosher salt and freshly ground black pepper.
Working in layers, evenly cover the tenderloin with the prosciutto slices, followed by the cooled mushroom mixture and the cheese.
Starting from the longest side, tightly roll the tenderloin into a pinwheel. Secure the roll with butcher’s twine at even intervals to prevent it from opening during cooking. Brush the exterior lightly with olive oil.
Heat a cast iron skillet over medium heat and add the remaining 1 tablespoon butter. Add the stuffed elk tenderloin and sear on all sides until nicely browned, about 4–5 minutes total.
Transfer the skillet to the oven and cook for 20 minutes, or until the internal temperature reaches medium-rare.
Remove the tenderloin from the skillet and transfer to a cutting board. Let rest for 10 minutes before slicing.
Slice and serve with roasted vegetables and a crisp green salad.