Preheat your oven to 400°F (200°C).
In a large mixing bowl, combine the cubed red potatoes, chicken chunks, broccoli florets, and sliced carrots.
In a separate bowl, whisk together the basil pesto, olive oil, ranch dry seasoning, minced garlic, Dijon mustard, chili powder, salt, and pepper.
Pour the flavorful mixture over the chicken and veggies. Toss everything together until well-coated.
Spread the coated chicken and veggie mixture evenly on a baking sheet.
Roast for about 25-30 minutes, or until the chicken is cooked through and the veggies are tender. Toss halfway through cooking.
In the last 5 minutes of roasting, sprinkle the freshly grated Parmesan cheese over the chicken and veggies.
Remove from the oven and let it cool for a few minutes before serving.