Place the potatoes, carrots, celery, onion, garlic, salt, parsley, Italian seasoning, and black pepper into a 4–6 quart slow cooker. Stir gently to combine.
In a small bowl, whisk together the chicken broth and cornstarch until smooth.
Pour the broth mixture into the slow cooker, then add the heavy cream and stir lightly.
Place the chicken breasts into the slow cooker and press them slightly into the liquid so they are mostly submerged.
Cover and cook on low for 6–7 hours, or until the potatoes are tender and the chicken is fully cooked.
Remove the chicken from the slow cooker and chop or shred it into bite-sized pieces.
Return the chicken to the pot and stir in the frozen peas and shredded Parmesan cheese.
Taste the stew and adjust seasoning if needed.
Serve the Slow Cooker Garlic Parmesan Chicken Stew warm, ideally with crusty bread for dipping.