In 10-inch nonstick skillet, heat oil over medium-high heat until hot. Cook turkey, onion and garlic in oil 6 to 8 minutes, stirring frequently, until turkey is well browned; drain.
In 3 1/2- to 4-quart slow cooker, mix cooked turkey mixture, pasta sauce and tomato paste.
Cover; cook on Low heat setting 4 to 5 hours or on High heat setting 2 hours.
To serve, spoon 1/2 cup turkey mixture onto bottom halves of rolls. Top each with half slice of cheese, cutting to fit. Cover with top halves of rolls.