Swiss chard joins the more expected carrot and celery in this rich-tasting broth. And because the dumplings are made with whole-wheat pizza dough, they’re easy to prep and better for you than the usual white-flour biscuits.
Melt butter in a Dutch oven over medium-high. Add carrots, celery, onion, and thyme; cook, stirring occasionally, until vegetables are slightly softened, 6 to 8 minutes. Add flour, and cook, stirring constantly, 1 minute. Gradually whisk in stock, 1 cup water, and salt. Add chicken, and bring to a boil, stirring often. Reduce heat to medium, and cook, stirring occasionally, until chicken is cooked through, vegetables are tender, and broth is thickened, about 10 minutes.
Meanwhile, roll dough to 1/8-inch thickness on a lightly floured surface. Using a 1 1/2-inch round cookie cutter, cut dough into 18 circles (discard dough scraps).
Add chard to Dutch oven, and cook, stirring often, until wilted, about 4 minutes. Increase heat to medium-high. When mixture reaches a low boil, drop dough pieces into Dutch oven, distributing over surface and stirring gently to cover with broth. Cook until dumplings are cooked through, 1 to 2 minutes.