Rub backstrap with olive oil, salt and pepper. Allow to rest at room temperature for 30 minutes. Heat olive oil in a medium skillet over medium-high heat. Add elk and brown on one side, about 3 minutes. Read CAUTION! below.
CAUTION! WARNING! DANGER! Adding alcohol to a hot pan or anywhere near an open flame WILL cause the alcohol to ignite. Be very careful. Keep your face, curtains and anything you don’t want to set on fire away from the pan.
Remove pan away from heat and add brandy, leeks, orange peel and garlic. Cook for 3 – 4 minutes more or until meat is rare to medium-rare. Remove meat and allow to rest for a few minutes. Add remaining brandy – SEE CAUTION! ABOVE. Cook for 2 minutes. Remove pan from heat and whisk in butter until melted. Slice backstrap into 1/4-inch thick medallions and spoon leek mixture over.