Preheat the oven to 400°F and line a large rimmed baking sheet with parchment paper for easy cleanup.
Trim the ends of the Brussels sprouts and slice them in half vertically, then place them in a bowl and toss with half of the olive oil, half of the sea salt, and half of the black pepper.
Arrange the sprouts cut-side down on the prepared baking sheet and roast for 20 to 25 minutes until the outer leaves are charred and the centers are tender.
While the sprouts roast, season the chicken breast on both sides with garlic powder, dried thyme, and the remaining salt and pepper.
Heat the remaining olive oil in a heavy-bottomed skillet over medium-high heat and sear the chicken for 6 to 8 minutes per side until the internal temperature reaches 165°F.
Remove the sprouts from the oven, drizzle with balsamic vinegar, and toss them directly on the pan to create a sticky glaze.
Allow the chicken to rest for 5 minutes before slicing it into strips and serving alongside the warm, glazed sprouts.