Preheat your oven to 400°F and line a baking sheet with parchment paper.
Trim the ends of the Brussels sprouts and cut them in half lengthwise.
Toss the sprouts on the baking sheet with half of the olive oil, half of the salt, and half of the pepper.
Roast for 20-25 minutes, tossing halfway through, until the edges are deeply browned and crispy.
While sprouts roast, season the chicken breast with garlic powder and the remaining salt and pepper.
Heat the remaining olive oil in a medium skillet over medium-high heat.
Sear the chicken for 6-7 minutes per side until the exterior is golden and the internal temperature reaches 165°F.
In a small bowl, whisk together the balsamic vinegar and honey until well combined.
Add the walnuts to the baking sheet with the sprouts for the final 5 minutes of roasting to toast them.
Remove the tray from the oven, drizzle the balsamic honey mixture over the sprouts and walnuts, and toss to coat.
Slice the chicken and serve it alongside the caramelized balsamic vegetables.