Preheat convection oven to 400 degrees Fahrenheit.
In a stainless steel bowl, whisk together olive oil, minced garlic, rosemary, thyme, salt, pepper, and paprika.
Arrange chicken cubes, halved potatoes, and carrot rounds in a 12-inch cast iron skillet.
Apply 50 percent of the herb-oil mixture to the skillet contents and toss to ensure uniform coating.
Transfer skillet to the center rack of the oven and roast for 15 minutes.
Introduce broccoli florets to the skillet and apply the remaining 50 percent of the herb-oil mixture.
Roast for an additional 15 minutes or until the core temperature of the poultry reaches 165 degrees Fahrenheit and potatoes are tender.
Remove from heat and allow for a 5-minute carry-over cooking period before service.