Preheat oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Dice the gold potato into 1-inch cubes and slice the carrots into half-moons.
Cut the chicken breast into even 1.5-inch pieces to ensure uniform cooking.
In a large bowl, whisk together the olive oil, minced garlic, chopped rosemary, thyme, salt, and pepper.
Add the chicken, potatoes, carrots, and broccoli florets to the bowl and toss thoroughly until every piece is coated in the herb oil.
Spread the mixture in a single layer on the prepared baking sheet, ensuring no overcrowding so the vegetables roast rather than steam.
Bake for 20-25 minutes, or until the chicken is cooked through and the potatoes are fork-tender and slightly browned.
Remove from the oven and let rest for 3 minutes before serving to keep the chicken juicy.