How to Make It
Combine baking powder and 2 cups of the flour in a bowl. Gradually stir in milk with a fork. Chill dough 20 minutes.
Heat butter in a large Dutch oven over medium. Add onion; cover and cook, stirring occasionally, until very soft, 15 to 20 minutes. Add 3 3/4 cups of the stock to Dutch oven, increase heat to high, cover and bring to a boil; let simmer 4 to 5 minutes. Whisk together remaining 1/4 cup stock and 2 tablespoons flour; stir into Dutch oven. Add squash and salt; cover. Simmer, stirring occasionally, until squash is very tender, 5 to 6 minutes.
Add squash mixture to a blender in batches. Remove center piece of blender lid (to allow steam to escape); secure lid on blender, and place a clean towel over opening in lid. Process each batch until very smooth. Return puree mixture to Dutch oven over medium-high. Add carrots, peas, corn, and thyme; cook, stirring occasionally, until boiling, 3 to 4 minutes.
Meanwhile, roll dough out onto a heavily floured surface to 1/8-inch thickness. Using a pizza cutter or a knife, cut into 1-inch squares. Add dumplings to simmering squash mixture, and cook, gently stirring occasionally, until slightly puffed, 3 to 4 minutes. Remove from heat. Stir in chives and pepper.