Preheat oven to 400 degrees Fahrenheit (200 degrees Celsius) and line a large baking sheet with parchment paper.
In a large mixing bowl, toss the diced potatoes with 2 tablespoons of olive oil, half of the salt, pepper, garlic powder, onion powder, and smoked paprika.
Spread the potatoes in a single layer on the prepared baking sheet and roast for 15 minutes.
While potatoes roast, toss the chicken cubes in the same mixing bowl with the remaining 1 tablespoon of olive oil and the remaining seasonings.
Remove the baking sheet from the oven, slide the potatoes to one side, and place the chicken cubes on the other side.
Return the tray to the oven and roast for 15 to 20 minutes until the chicken reaches an internal temperature of 165 degrees Fahrenheit.
During the final 5 minutes of roasting, steam the broccoli florets in a microwave-safe bowl with a splash of water for 3 minutes or until tender-crisp.
Divide the chicken, potatoes, and broccoli equally into four meal prep containers and allow to cool before sealing.