Preheat oven to 400 degrees Fahrenheit (200 degrees Celsius).
In a large mixing bowl, combine the cubed potatoes and sliced carrots.
Add the olive oil, minced garlic, oregano, rosemary, salt, and black pepper to the bowl and toss to coat thoroughly.
Spread the potatoes and carrots in a single layer on a large rimmed baking sheet.
Roast for 15 minutes.
Add the zucchini to the bowl with any remaining oil and herb mixture, toss, then add to the baking sheet with the other vegetables.
Continue roasting for another 15 to 20 minutes until potatoes are tender and golden brown.
Remove from oven and garnish with fresh parsley before serving.