Preheat your oven to 400 degrees Fahrenheit and line a large rimmed baking sheet with parchment paper.
Peel the batata and cut into half-inch cubes, then dice the chicken breast into similar bite-sized pieces.
In a large mixing bowl, combine the batata, chicken, and broccoli florets.
Drizzle with olive oil and add the minced garlic, chopped rosemary, thyme, sea salt, and black pepper.
Toss everything thoroughly until the ingredients are evenly coated in the oil and herbs.
Spread the mixture in a single layer on the prepared baking sheet, ensuring the pieces are not overcrowded.
Roast for 22 to 25 minutes, tossing halfway through, until the chicken is cooked through and the batata is fork-tender.
Remove from the oven and serve immediately in a wide bowl.