Place the chicken breasts in the slow cooker. Add the sliced carrots, sliced celery, diced onion, chicken broth, thyme, salt, and black pepper.
Cover and cook on low for 6 hours or high for 3 hours until the chicken is fully cooked and the vegetables are tender.
Remove the chicken, shred it with two forks, and return it to the slow cooker.
Stir in the heavy cream and the cornstarch slurry. Cook on high for 20 more minutes until the filling thickens.
While the filling thickens, bake the buttermilk biscuits according to package or recipe directions until golden.
Spoon the filling into bowls and top each serving with a warm biscuit.