Cook the pasta according to package directions.
Heat the oil in a large saucepan over medium heat. Add the garlic and cook, stirring, for 1 minute. Add the tomatoes and cook until they begin to break down and release their juices, about 2 minutes. Stir in the chard stems and cook until softened, about 3 minutes. Add the chard leaves, cannellini beans, 1/2 teaspoon salt, and the red pepper and cook, stirring, until the chard leaves are tender, 3 to 5 minutes.
Divide the cooked pasta among individual bowls and top with the chard mixture and Parmesan.