Wash the baby potatoes, cut them in half, and mince the garlic cloves.
Rub the chicken breasts with olive oil, then season both sides evenly with Italian seasoning, salt, black pepper, and red pepper flakes if using.
Arrange the halved potatoes in an even layer across the bottom of the slow cooker.
Place the seasoned chicken breasts in a single layer over the potatoes without stacking them.
Pour the chicken broth around the chicken and over the potatoes.
Scatter the minced garlic evenly over the chicken, then sprinkle the grated Parmesan cheese across the top.
Cover and cook on low for 6 to 7 hours or on high for 3 to 4 hours without repeatedly lifting the lid.
Check the thickest part of each chicken breast with an instant-read thermometer and remove the chicken when it reaches 165°F.
Pierce the potatoes with a fork to confirm they are tender, allowing them to cook for an additional 15 to 20 minutes if needed.
Transfer the chicken and potatoes to a serving dish, spoon the garlic-Parmesan cooking liquid over the top, and garnish with chopped parsley if desired.