Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper for easy cleanup.
Trim the woody ends off the Brussels sprouts and slice each one in half vertically.
In a medium bowl, toss the halved sprouts with 0.5 tbsp of olive oil, 0.125 tsp sea salt, and 0.125 tsp black pepper until evenly coated.
Spread the sprouts in a single layer on the prepared baking sheet, ensuring they are not crowded so they crisp up properly.
Roast the sprouts for 20-25 minutes, tossing halfway through, until the outer leaves are golden brown and crispy.
While the sprouts roast, season the chicken breast on both sides with the garlic powder and the remaining sea salt and black pepper.
Heat the remaining 0.5 tbsp of olive oil in a heavy-bottomed skillet over medium-high heat.
Place the chicken in the skillet and sear for 6-7 minutes per side, or until the internal temperature reaches 165°F and the outside is nicely browned.
Remove the roasted sprouts from the oven, transfer them to a clean bowl, and toss with the balsamic glaze while they are still hot.
Slice the seared chicken into strips and serve immediately alongside the warm, glazed Brussels sprouts.