Place the chicken breasts in the bottom of the slow cooker. Add the diced onion, sliced carrots, celery, and minced garlic around the chicken.
Pour in the chicken broth and cream of chicken soup. Add the dried thyme, salt, and black pepper. Stir gently around the chicken to combine the liquid.
Cover and cook on low for 6 to 7 hours or on high for 3 to 4 hours, until the chicken is fully cooked and tender.
Remove the chicken, shred it with two forks, and return it to the slow cooker. Stir to combine with the soup.
Tear each biscuit into 3 to 4 rough pieces and drop them on top of the simmering soup. Add the frozen peas.
Cover and cook on high for 1 to 1.5 hours, until the dumplings are puffed and cooked through in the center.
Gently stir, ladle into bowls, and garnish with fresh chopped parsley before serving.