Preheat oven to 400 degrees Fahrenheit (200 degrees Celsius).

In a large mixing bowl, toss potato wedges with 1.5 tablespoons olive oil, 1 tablespoon Cajun seasoning, and half of the minced garlic.

Coat chicken thighs with the remaining olive oil, Cajun seasoning, minced garlic, salt, and pepper in a separate bowl.

Arrange chicken thighs and potato wedges in a single layer on a large rimmed baking sheet.

Roast for 35 to 40 minutes or until the chicken reaches an internal temperature of 165 degrees Fahrenheit (74 degrees Celsius).

Evenly sprinkle Parmesan cheese over the chicken and potatoes during the final 5 minutes of cooking time.

Remove from oven and garnish with fresh parsley before serving.