On a cutting board, slice the elk top sirloin roast into 6–8 thin steaks, about 1/4 inch thick. Season lightly with salt and pepper and set aside.
In a small bowl, combine shallots, garlic, Parmesan cheese, parsley, and 2 tablespoons olive oil. Spread about 1 tablespoon of the mixture evenly over each piece of meat.
Starting at the longest end, roll up each steak into a pinwheel shape and secure with a piece of butcher’s twine.
Heat a skillet over medium heat and add the butter and remaining 2 tablespoons olive oil. Lightly dredge each rolled steak in flour, shake off excess, and place in the skillet. Brown the meat, turning every 2 minutes for a total of 6 minutes.
Add the orzo pasta and beef broth to the skillet. Bring to a boil, then reduce heat to low and simmer for 20–25 minutes, until the pasta is tender and the meat is cooked through.
Remove the twine, serve immediately, and enjoy.