Preheat the oven to 425 degrees Fahrenheit. Line a large rimmed sheet pan with parchment paper or foil for easier cleanup.
In a large bowl, toss the potatoes with olive oil, garlic, parmesan, salt, and pepper. Spread them evenly over one third of the sheet pan. Roast for 15 minutes to give them a head start.
While the potatoes cook, toss the chicken with olive oil, garlic, parmesan, breadcrumbs, Italian seasoning if using, salt, and pepper. Coat evenly so the parmesan adheres well.
Remove the pan from the oven. Push the potatoes to one side and arrange the chicken on another third of the pan.
In the same bowl, toss the green beans with olive oil, garlic, salt, and pepper. Spread them over the remaining third of the pan.
Return the pan to the oven and bake for 25 to 30 minutes, or until the chicken reaches an internal temperature of 165 degrees Fahrenheit.
For extra crispy potatoes, switch the oven to broil for 3 to 4 minutes at the end of cooking. Allow the chicken to rest for 5 minutes before serving.