Preheat oven to 400 degrees Fahrenheit (200 degrees Celsius).
Line a large rimmed baking sheet with parchment paper or aluminum foil.
Place the cubed chicken, broccoli, bell pepper, and zucchini onto the prepared baking sheet.
Drizzle olive oil over the chicken and vegetables.
Sprinkle garlic powder, oregano, salt, and black pepper evenly over the ingredients.
Toss the mixture until all components are thoroughly coated in oil and seasoning, then spread into a single, even layer.
Roast for 20 to 25 minutes until the chicken reaches an internal temperature of 165 degrees Fahrenheit (74 degrees Celsius) and vegetables are tender.
Garnish with grated parmesan cheese prior to serving.