In medium-size bowl, whisk together the mayonnaise and olive oil. Stir in the garlic, Parmesan cheese, pepper and parsley (you should have about 1 cup). Cover; refrigerate for at least 1 hour.
Season the slices of beef tenderloin with the salt and pepper. In a large skillet, heat the oil over high heat. Add the beef; cook for 1 minute on each side or until browned and cooked through. Remove to warm platter. Serve immediately with aioli, and prepared refrigerated mashed potatoes, if desired. Makes 6 servings.
