Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Peel the sweet potato and cut into 1/2-inch cubes, then place them in a mixing bowl.
Toss the sweet potato cubes with half of the olive oil, dried rosemary, dried thyme, and a pinch of salt and pepper.
Spread the sweet potatoes in a single layer on the baking sheet and roast for 15 minutes.
Add the broccoli florets to the baking sheet, tossing with the sweet potatoes, and roast for an additional 10-12 minutes until tender.
While the vegetables roast, season the chicken breast with the remaining salt and pepper.
Heat the remaining olive oil in a skillet over medium-high heat and sear the chicken for 6-7 minutes per side until the internal temperature reaches 165°F.
During the last 2 minutes of cooking the chicken, add the minced garlic to the skillet and stir constantly until it becomes golden and fragrant.
Slice the chicken breast and serve it alongside the roasted caramelized garlic herb sweet potatoes and broccoli.