Add the scallion bulbs and garlic and cook, stirring occasionally, for 2 minutes. Add the Swiss chard, black-eyed peas, water, broth, Tabasco, and salt to the pot. Bring to a boil.

Stir in peas, cream, butter, reserved pasta and Broccolini, and 1/2 cup reserved pasta cooking liquid. Cook, stirring often, until sauce thickens and coats pasta, about 3 minutes.