Preheat oven to 400°F and line a baking sheet with parchment paper.
Trim the ends of the Brussels sprouts and slice them in half lengthwise.
Toss the sprouts with 0.5 tbsp olive oil, 0.125 tsp sea salt, and 0.125 tsp black pepper.
Roast the sprouts for 20 minutes until the outer leaves are slightly charred and tender.
Season the chicken breast with garlic powder and the remaining salt and pepper.
Heat the remaining 0.5 tbsp olive oil in a skillet over medium-high heat.
Cook the chicken for 6-8 minutes per side until the internal temperature reaches 165°F.
Whisk the balsamic vinegar and honey together in a small bowl to create a glaze.
Add the walnuts to the roasting pan during the last 5 minutes of cooking.
Remove sprouts from the oven and toss immediately with the balsamic glaze.
Slice the chicken and serve alongside the warm, caramelized sprouts and walnuts.