Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
Trim the ends of the Brussels sprouts and cut them in half; peel and slice the carrots into 1/2-inch thick rounds.
Place the vegetables on the baking sheet, drizzle with 0.5 tbsp of olive oil, and sprinkle with half of the salt, pepper, and thyme. Toss to coat evenly.
Roast the vegetables for 20-25 minutes, tossing halfway through, until they are tender and slightly caramelized.
While the vegetables roast, mince the garlic and season the chicken breast on both sides with the remaining salt, pepper, and thyme.
Heat the remaining 0.5 tbsp of olive oil in a medium skillet over medium-high heat. Once hot, add the chicken breast.
Sear the chicken for 5-7 minutes per side, or until the internal temperature reaches 165°F. Add the minced garlic to the pan during the last 2 minutes of cooking for extra flavor.
Remove the chicken from the pan and let it rest for 5 minutes before slicing.
Serve the sliced chicken alongside the roasted vegetables for a clean, nutrient-dense meal.