Preheat your oven to 400°F and line a large rimmed baking sheet with parchment paper for easy cleanup.
Trim the ends off the Brussels sprouts and slice them in half vertically, then toss them on the baking sheet with half of the olive oil, sea salt, and black pepper.
Spread the sprouts in a single layer, cut-side down, 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 with the remaining salt and pepper, then sear in a skillet with the rest of the olive oil over medium-high heat for 6-7 minutes per side until golden and cooked through.
In a small saucepan over medium-low heat, whisk together the balsamic vinegar, honey, and minced garlic, simmering for about 5 minutes until it reduces into a thick, syrupy glaze.
Place the walnuts in a small dry pan over medium heat for 2-3 minutes, tossing frequently until they are fragrant and lightly toasted.
Slice the chicken into strips and combine with the roasted Brussels sprouts in a bowl, drizzling the warm balsamic glaze over the top and finishing with the toasted walnuts.