Rinse and drain chard; pat dry with paper towels. Remove stems and center ribs from chard, and cut ribs and stems crosswise into 1/4-inch slices. Cut chard leaves into 1-inch strips.
Heat a Dutch oven over medium heat. Add pancetta; cook 6 minutes or until browned. Add onion and garlic, and cook 10 minutes or until lightly browned, stirring frequently. Add chard stems, and cook 3 minutes, stirring frequently. Add chard leaves and red pepper; cook 5 minutes or until chard wilts, tossing frequently.
Cook pasta according to package directions, omitting salt and fat. Drain the pasta in a colander over a bowl; reserve 1/4 cup pasta water. Add reserved pasta water and pasta to chard mixture; cook over medium-high heat 1 minute, stirring frequently. Stir in 1/4 cup cheese. Add parsley, salt, and black pepper; toss well to combine. Sprinkle with 1/2 cup cheese.