Dice the yellow onion into 1/2-inch pieces, chop the carrots and celery into bite-sized pieces, and peel and cut the potatoes into 1-inch chunks. Freshly mince all 8 garlic cloves—I always use fresh garlic rather than pre-minced because it makes a noticeable difference in the soup's flavor depth. Pat the chicken breasts dry with paper towels and season generously on both sides with kosher salt, cracked black pepper, and Italian seasoning. Having everything prepped and ready before cooking ensures a smooth workflow.
Add the seasoned chicken breasts, diced onion, chopped carrots, celery, minced garlic, and potato chunks to your slow cooker in any order. Pour the chicken broth over everything and stir gently to distribute the ingredients evenly. The broth will provide the foundation for all the flavors to meld together during the long, slow cooking process.
Cover and cook on high for 2-3 hours or on low for 4-5 hours, until the chicken is completely cooked through and tender enough to shred easily. The longer, slower cooking allows the chicken to become incredibly tender and all the flavors to develop fully. After cooking is complete, carefully remove the chicken breasts from the slow cooker and set them on a cutting board.
Using two forks or your hands, shred the cooked chicken into bite-sized pieces and return it to the slow cooker. In a small bowl, whisk together the cornstarch and heavy cream until completely smooth with no lumps—this prevents the cornstarch from clumping when it hits the hot broth. Slowly pour the cornstarch mixture into the slow cooker while stirring constantly to incorporate it evenly throughout the soup.
Stir in the parmesan cheese until it's fully melted and incorporated into the creamy broth. I prefer using Sartori brand for its nutty, high-quality finish, which really elevates the final taste. Cook on high for 20-30 minutes, stirring occasionally, until the soup thickens slightly and the flavors are fully developed.
Ladle the hot soup into bowls and garnish each serving with freshly chopped parsley. Serve immediately with crusty bread on the side for dipping and soaking up every bit of this rich, creamy soup.