Preheat oven to 400°F (200°C) and lightly grease a large rimmed baking sheet.
In a large mixing bowl, combine the quartered potatoes with 2 tablespoons of olive oil, half of the minced garlic, salt, and pepper.
Spread the potatoes in a single layer on the prepared baking sheet and roast for 15 minutes.
While potatoes are roasting, toss the chicken pieces in the same mixing bowl with the remaining olive oil, garlic, oregano, and basil.
Remove the baking sheet from the oven and move the potatoes to one side.
Place the chicken pieces on the other side of the pan in a single layer.
Sprinkle half of the Parmesan cheese over both the chicken and potatoes.
Return the pan to the oven and bake for 15 to 20 minutes, or until the chicken reaches an internal temperature of 165°F (74°C) and the potatoes are fork-tender.
Remove from oven, sprinkle with the remaining Parmesan cheese and fresh parsley, and serve immediately.