Preheat your oven to 400°F 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 sprouts with 0.25 tbsp of the olive oil, sea salt, and black pepper until evenly coated.
Spread the sprouts in a single layer on the baking sheet and roast for 20-25 minutes until they are tender and the outer leaves are charred.
Season the chicken breast lightly with additional sea salt and black pepper.
Heat the remaining 0.25 tbsp of olive oil in a skillet over medium-high heat and sear the chicken for 6-8 minutes per side until fully cooked.
While the chicken rests, combine the balsamic vinegar, maple syrup, and minced garlic in a small saucepan over low heat.
Simmer the balsamic mixture for 3-5 minutes until it thickens into a glossy glaze.
Toast the walnut halves in a dry pan over medium heat for 2-3 minutes until they become fragrant and slightly golden.
Toss the roasted sprouts with the toasted walnuts and the balsamic glaze, then serve immediately alongside the pan-seared chicken.