Preheat oven to 400°F (200°C) and lightly grease a large rimmed baking sheet.
In a small bowl, whisk together the melted butter, olive oil, minced garlic, and dried oregano.
Arrange the cubed chicken and halved potatoes on the baking sheet. Drizzle with half of the garlic butter mixture and season with salt and pepper. Toss to coat and spread into a single layer.
Roast in the preheated oven for 15 minutes.
Remove the pan from the oven and add the broccoli florets. Drizzle the remaining garlic butter mixture over the broccoli and toss everything together.
Return the pan to the oven and roast for an additional 10-12 minutes, or until the chicken is cooked through to an internal temperature of 165°F (74°C) and the potatoes are fork-tender.
Garnish with fresh parsley and serve immediately.