Sprinkle the garlic, celery, carrots, and onion into the bottom of a 6- to 8-quart slow cooker. Add the chicken soup, mushroom soup, and broth, and whisk together. Add the chicken, cover, and cook for 2 hours on high.

After 2 hours, remove the chicken to a cutting board. When cool enough to handle, shred the meat with a fork. Return the shredded chicken to the slow cooker, and add the peas.

Lay the biscuits out on a clean work surface. Sprinkle with the cheddar and chives, lightly pressing the cheese and chives into the biscuits to adhere. Cut each biscuit into fourths and place them on the surface of the soup. Cover and cook until the biscuits are cooked through, 20 to 30 minutes. Serve the soup topped with parsley.