Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Trim the ends off the Brussels sprouts and slice them in half; peel the carrots and cut them into 1/2-inch thick rounds.
Place the vegetables on the baking sheet and toss with 0.5 tablespoon of olive oil, half of the sea salt, half of the black pepper, and all of the dried thyme.
Spread the vegetables in a single layer and roast for 20-25 minutes, tossing halfway through, until they are tender and caramelized on the edges.
While the vegetables roast, pat the chicken breast dry with paper towels and season both sides with garlic powder and the remaining salt and pepper.
Heat the remaining 0.5 tablespoon of olive oil in a cast-iron or stainless steel skillet over medium-high heat.
Place the chicken in the hot skillet and sear for 6-7 minutes per side, or until the internal temperature reaches 165°F and the exterior is beautifully browned.
Remove the chicken from the pan and let it rest for 5 minutes to lock in the juices before slicing and serving alongside the roasted vegetables.