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, and peel and slice the carrots into half-inch rounds.
Toss the vegetables on the baking sheet with 1 tablespoon of olive oil and half of the salt, pepper, and dried thyme.
Spread the vegetables in a single layer and roast for 20-25 minutes until they are tender and show dark, caramelized edges.
While the vegetables roast, pat the chicken breast dry and season both sides with the remaining salt, pepper, garlic powder, and thyme.
Heat the remaining 0.5 tablespoon of olive oil in a heavy-bottomed 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 crust is golden brown.
Remove the chicken from the pan and let it rest for 5 minutes to lock in the juices before slicing.
Plate the sliced chicken alongside the roasted vegetables and serve immediately.