Start by placing the 2 pounds of boneless, skinless chicken thighs into your slow cooker. No need to cut them up; they will become shreddable as they cook.
Chop 1 medium onion, slice 2 carrots, and slice 2 celery stalks. Add all of these to the slow cooker along with 3 cloves of minced garlic.
Sprinkle in 1 teaspoon of dried thyme, 1 teaspoon of dried parsley, 1/2 teaspoon black pepper, and 1/4 teaspoon salt. Pour in 4 cups of low-sodium chicken broth and add 1 can of cream of chicken soup. Stir it all together gently to combine.
Cover the slow cooker and set it to cook on low for 6-8 hours or on high for 4-5 hours. The chicken should be tender and easy to shred by the end of the cooking time.
About 30 minutes before serving, it's time to whip up the dumplings. In a mixing bowl, combine 1 cup of whole wheat flour, 1 tablespoon of baking powder, and 1/2 teaspoon of salt. In a separate bowl, whisk together 1/2 cup of milk, 1/4 cup of melted butter, and 1 egg. Pour the wet ingredients into the dry ingredients and mix until just combined.
Once the chicken is cooked, carefully remove it from the slow cooker and shred it with two forks. Return the shredded chicken back to the pot and stir in 1 cup of frozen peas. Scoop spoonfuls of the dumpling mixture onto the top of the chicken mixture. Cover and cook on high for an additional 30 minutes, or until the dumplings are fluffy and cooked through.