Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper for easy cleanup.
Prepare the vegetables by dicing the sweet potato into 1/2-inch cubes, slicing the carrots into thin rounds, and chopping the broccoli into bite-sized florets.
Cut the chicken breast into even 1-inch chunks to ensure they cook at the same rate as the vegetables.
In a large mixing bowl, whisk together the extra virgin olive oil, sea salt, black pepper, garlic powder, dried rosemary, and ground turmeric until well combined.
Add the chicken and all the prepared vegetables to the bowl, tossing thoroughly until every piece is evenly coated in the golden herb oil.
Spread the mixture in a single layer across the prepared baking sheet, making sure not to overcrowd the pan so the vegetables roast rather than steam.
Roast in the center of the oven for 20 to 25 minutes, tossing halfway through, until the chicken is cooked through and the vegetables are tender and golden brown.