In a large bowl, combine the chicken thighs, olive oil, minced garlic, Italian seasoning, salt, and black pepper. Toss to coat the chicken evenly with the seasonings.
Place the halved baby potatoes in the bottom of a slow cooker. Layer the seasoned chicken thighs on top of the potatoes.
In a separate bowl, whisk together the chicken broth, heavy cream, and grated Parmesan cheese until well combined. Pour this mixture over the chicken and potatoes in the slow cooker.
Cover and cook on low for 6-7 hours or on high for 3-4 hours, until the chicken is cooked through and tender.
Once cooked, carefully remove the chicken and potatoes from the slow cooker and place them on a serving platter.
If desired, stir the sauce in the slow cooker to combine and thicken slightly. Pour the sauce over the chicken and potatoes.
Garnish with fresh parsley before serving.