Lightly grease the basin of a 6-quart slow cooker with non-stick spray.
In a medium mixing bowl, whisk together the olive oil, minced garlic, oregano, basil, salt, and black pepper to create the marinade.
Place the cubed chicken and quartered potatoes into the slow cooker.
Pour the marinade over the chicken and potatoes, tossing thoroughly with a spatula to ensure even distribution of fats and aromatics.
Secure the lid and cook on the 'Low' setting for 6 hours or the 'High' setting for 3.5 hours, until the potatoes are fork-tender and the chicken has reached an internal temperature of 165°F (74°C).
Switch the slow cooker to the 'Keep Warm' setting and sprinkle the grated Parmesan cheese evenly over the surface.
Cover for 5 minutes to allow the cheese to melt and adhere to the ingredients.
Garnish with chopped fresh parsley and serve immediately.