Add the chicken breasts, chicken broth, diced tomatoes, Italian seasoning, and minced garlic to the slow cooker. Cover and cook on low for 6 hours until the chicken is tender.
Remove the chicken from the slow cooker and shred it with two forks. Return the shredded chicken to the pot.
Stir in the heavy cream and 3/4 cup of the grated Parmesan cheese until combined.
Cut each biscuit into four pieces and gently drop them into the slow cooker. Stir lightly to submerge most of the pieces.
Cover and cook on high for 1 hour until the biscuit pieces are cooked through and tender.
Taste and add salt and black pepper as needed. Serve hot with the remaining Parmesan cheese and chopped parsley sprinkled on top.