Add chicken breasts, peas, corn, carrots, onion, celery, garlic, thyme, bay leaves, bouillon cubes, nutmeg, salt, pepper, and chicken broth to the slow cooker.
Cook on low for 4–6 hours until chicken reaches an internal temperature of 165°F and vegetables are tender.
Remove chicken breasts and shred with two forks. Discard thyme sprigs and bay leaves.
Return shredded chicken to slow cooker. Stir in gnocchi, cream of mushroom soup, and ½ cup heavy cream.
In a small bowl, whisk cornstarch into remaining ¼ cup heavy cream until smooth. Stir slurry into soup.
Cook on low for an additional 30 minutes, stirring halfway through, until soup thickens.
Adjust seasoning with salt, pepper, and additional pinch nutmeg. Serve warm with biscuits.