Cook greens in boiling water to cover in a Dutch oven 10 minutes. Drain and set aside.
Cook bacon in Dutch oven until crisp; remove and drain on paper towels, reserving 2 tablespoons drippings in skillet.
Sauté onion and garlic in hot drippings until tender. Add greens, roasted red peppers, and next 3 ingredients; cook over medium heat, stirring occasionally, 5 minutes or until thoroughly heated.
Heat cream in a small saucepan over medium heat 5 minutes or until thoroughly heated (do not boil). Set aside 2 tablespoons Parmesan cheese. Stir in remaining cheese until melted. Toss together cream mixture and pasta.
Top pasta with greens mixture; sprinkle with bacon and reserved cheese. Garnish, if desired.
*16 ounces mustard greens may be substituted for turnip greens. Cook 10 to 15 more minutes.