Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
Trim and halve the Brussels sprouts and peel and slice the carrots into half-inch rounds.
In a large bowl, toss the Brussels sprouts and carrots with half of the olive oil, half of the minced garlic, half of the rosemary, half of the thyme, and a pinch of salt and pepper.
Spread the vegetables in a single layer on the prepared baking sheet and roast for 20 to 25 minutes until tender and caramelized.
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.
Add the chicken to the skillet and sear for 6 to 7 minutes per side, or until the internal temperature reaches 165°F.
During the last 2 minutes of cooking the chicken, add the remaining garlic, rosemary, and thyme to the pan to release their aromatics.
Drizzle the lemon juice over the chicken and vegetables before serving.