Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Trim the Brussels sprouts and cut them in half, then slice the carrots into 1/2-inch rounds and the red onion into small wedges.
In a large bowl, toss the Brussels sprouts, carrots, and onion with 1 tablespoon of olive oil, dried thyme, half of the salt, and half of the pepper.
Spread the vegetables in a single layer on the prepared baking sheet and roast for 20-25 minutes, tossing halfway through, until tender and caramelized.
While the vegetables roast, pat the chicken breast dry with paper towels and season both sides with the remaining salt and pepper.
Heat the remaining 0.5 tablespoon of olive oil in a stainless steel or cast-iron skillet over medium-high heat.
Place the chicken in the skillet and sear for 6-7 minutes on the first side until a golden crust forms, then flip and cook for another 5-6 minutes until the internal temperature reaches 165°F.
Add the minced garlic to the pan during the last 60 seconds of cooking, stirring constantly to avoid burning.
Remove the chicken from the heat and let it rest for 5 minutes to lock in the juices.
Plate the chicken alongside the roasted vegetables and finish with a fresh squeeze of lemon juice over the entire dish.