Cook sausage in hot oil in a skillet over medium heat 5 minutes or until browned. Remove from skillet; set aside.
Sauté onion and next 3 ingredients in skillet 5 minutes or until tender. Add wine and garlic; cook 2 minutes or until liquid evaporates. Remove from heat.
Stir together mashed potatoes and 1 cup hot water in a large bowl; stir in sausage, onion mixture, parsley, thyme, and nutmeg.
Place steak between 2 sheets of heavy-duty plastic wrap; flatten to 1/4- to 1/2-inch thickness using a meat mallet or rolling pin. Spread potato mixture evenly over flank steak, leaving a 1/2-inch border.
Roll steak, jellyroll fashion, starting with a long side; secure with string. Place on a lightly greased rack in a broiling pan.
Bake at 425° for 10 minutes; reduce heat to 375°. Bake 25 to 30 minutes or to desired degree of doneness.