Preheat your oven to 400°F (200°C).
Trim the Brussels sprouts and halve them; peel and slice the carrots into rounds, and cut the red onion into small wedges.
Toss the Brussels sprouts, carrots, and red onion on a baking sheet with half of the olive oil, half of the sea salt, and half of the black pepper.
Roast the vegetables for 20-25 minutes, tossing halfway through, until they are tender and have developed charred, crispy edges.
While the vegetables roast, season the chicken breast evenly on both sides with the remaining sea salt, black pepper, and dried thyme.
Heat the remaining olive oil in a stainless steel or cast-iron skillet over medium-high heat.
Place the chicken in the hot skillet and sear for 5-7 minutes per side, or until the internal temperature reaches 165°F and the exterior is golden brown.
Add the minced garlic to the pan during the last 60 seconds of cooking to infuse the oil without burning.
Remove the chicken from the heat, drizzle with fresh lemon juice, and serve immediately alongside the roasted vegetable medley.