Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Trim the ends off the Brussels sprouts and cut them in half lengthwise to ensure maximum surface area for caramelization.
Toss the sprouts on the baking sheet with 0.5 tablespoons of olive oil, 0.125 teaspoons of sea salt, and 0.125 teaspoons of black pepper.
Roast the sprouts for 20 to 25 minutes, flipping halfway through, until the edges are deeply charred and crispy.
While the sprouts roast, season the chicken breast evenly with the remaining sea salt and black pepper.
Heat the remaining 0.25 tablespoons of olive oil in a medium skillet over medium-high heat.
Sear the chicken for 6 to 7 minutes per side until the internal temperature reaches 165°F, then set aside to rest for 5 minutes before slicing.
In a small saucepan over low heat, whisk together the balsamic vinegar and honey, simmering for 3 to 5 minutes until the liquid reduces into a thick, velvety glaze.
Stir the minced garlic and red pepper flakes into the balsamic glaze during the last minute of simmering.
Toss the roasted Brussels sprouts in the warm balsamic glaze, then serve immediately alongside the sliced chicken and garnish with the walnuts.