Place the baby potatoes in the bottom of a 6-quart slow cooker, cutting them into roughly 1-inch pieces so they cook evenly. Drizzle with the oil, then season with the salt, pepper, and garlic powder and toss to coat.
Add the chicken pieces on top of the potatoes. Season with the salt, pepper, garlic powder, and onion powder, then scatter the minced garlic evenly over the top.
In a medium bowl, whisk together the Caesar dressing and chicken broth, then pour it evenly over the chicken and potatoes. Scatter the cubed cream cheese over everything and sprinkle with the Italian seasoning.
Cover and cook on LOW for 4-5 hours or HIGH for 2 1/2-3 1/2 hours, until the potatoes are fork-tender and the chicken reaches an internal temperature of 165F.
Gently stir everything together, breaking up any remaining cream cheese, until the sauce is smooth and creamy. Stir in the Parmesan until it melts into the sauce and everything is coated.
Lay the provolone slices evenly over the top, overlapping slightly, then cover and cook another 10-15 minutes on LOW, until the cheese is melted and gooey.
Sprinkle with the fresh parsley and a little more Parmesan, then serve warm.