In 8-inch skillet, cook sausage over medium heat, stirring occasionally, until no longer pink; drain if necessary. Cool. Meanwhile, place flank steaks between pieces of plastic wrap or cooking parchment paper; gently pound with flat side of meat mallet until steaks are rectangular and about 1/4 inch thick. Arrange 3 to 4 prosciutto slices on each steak, covering surface.
Add stuffing, parsley, cheese and egg to sausage in skillet; stir well. Spoon evenly over prosciutto on each steak, leaving 1/4-inch border on all sides. Starting at a long side, roll up 1 steak, tucking in ends to enclose stuffing; secure with kitchen string in 2 or 3 places. Repeat with second steak.
Spray 5-quart slow cooker with cooking spray. Place steak rolls, seam sides down, in slow cooker. Sprinkle dried minced garlic over steak rolls; spoon pasta sauce over garlic.
Cover; cook on Low heat setting 5 to 6 hours.
Carefully remove steak rolls; clip and discard string. Slice meat crosswise into pieces. Serve with sauce from slow cooker.