Mix together the dry ingredients in a large mixing bowl.
Then, use forks or a pastry cutter to cut the cold butter into the dry ingredients until the butter pieces are the size of small peas.
Pour in the 100-115g/1/2 cup sourdough starter discard and milk. Combine milk, starter, and flour mixture until the dry mixture has absorbed the liquids.
You may need to use a spatula or dough scraper to clean the sides of the bowl.
Once all the ingredients are well combined into a dough, cover the bowl with plastic wrap or another cover. Leave at room temperature 2 to 8 hours to ferment before you make your soup.
First, melt the butter in a large soup pot or dutch oven (at least 5-quart capacity). Add your onion and sauté until the pieces are beginning to soften then add the celery.
Continuing stirring and sautéing until onions are becoming translucent.
Add the chicken breasts and begin to cook the outsides with the onions and celery. Add the thyme to draw out the fragrance and flavor during the sautéing stage. Turn the chicken to make sure that the outsides get seared.
Add your salt, pepper, and chicken broth and bring the liquid to a boil. Add the carrots and, if using, the broccoli. Optional: add a bay leaf to the broth to deepen the flavors of the soup as it cooks. Cover the pot and reduce to a simmer over low heat for 12 minutes.
After your timer has gone off, add your peas if you are using them. Bring the chicken soup back to a boil.
Then, drop in your sourdough discard dumplings by heaping tablespoon portions until the balls of dough are scattered evenly over the soup.
Cover the large pot, then reduce the heat to a high simmer or low boil for 18 to 20 minutes. When dumpling balls are fully cooked, they should be puffy and a toothpick inserted into one should come out clean.
Use a fork to transfer the cooked chicken to a large bowl. Shred the chicken until its cut into smaller bite-size pieces (about 1/2-inch pieces).
Remove the pot from heat then ladle into bowls to serve.