Prepare the chicken by patting the boneless skinless chicken breasts dry with paper towels so the seasonings will stick well.
Place the halved baby potatoes in the bottom of the crockpot, spreading them into an even layer to create a bed for the chicken.
In a small bowl, combine the salt, black pepper, dried Italian seasoning, and paprika, stirring to mix the spices evenly.
Drizzle the olive oil over the chicken breasts, then sprinkle the mixed seasonings evenly on both sides of the chicken, gently rubbing them in.
Arrange the seasoned chicken breasts in a single layer on top of the baby potatoes in the crockpot.
Sprinkle the minced garlic evenly over the chicken and potatoes so the flavor spreads through the whole dish as it cooks.
Pour the low-sodium chicken broth around the sides of the crockpot, being careful not to wash the seasonings off the chicken.
Cover the crockpot with the lid and cook on LOW for about 4 hours, or until the chicken is cooked through and the potatoes are tender when pierced with a fork.
Once the chicken and potatoes are cooked, pour the heavy cream into the crockpot around the chicken, then gently stir the cream into the cooking liquid without breaking up the potatoes too much.
Add the freshly grated Parmesan cheese to the crockpot and stir gently again until the cheese begins to melt into the creamy sauce.
Dot the top of the chicken and potatoes with the small pieces of unsalted butter, then cover and cook on LOW for another 15 to 20 minutes to let the sauce thicken slightly.
Before serving, taste the sauce and adjust the seasoning with a little extra salt or black pepper if needed.
Sprinkle the chopped fresh parsley over the finished Garlic Parmesan Crockpot Chicken and Potatoes for a fresh, bright touch, then serve warm straight from the crockpot.