Trim the ends off the Brussels sprouts and slice them in half vertically.
Season the chicken breast evenly on both sides with the sea salt, black pepper, and garlic powder.
Heat 0.5 tbsp of the olive oil in a large skillet over medium-high heat.
Add the chicken to the skillet and cook for 6 to 7 minutes per side until the internal temperature reaches 165°F, then remove and let rest.
In the same skillet, add the remaining 0.25 tbsp of olive oil and the Brussels sprouts, placing them cut-side down.
Sear the sprouts for 4 to 5 minutes without moving them until the bottoms are deeply caramelized and tender.
While the sprouts cook, roughly chop the walnuts and toast them in a small dry pan for 2 minutes until fragrant.
Whisk together the balsamic vinegar and honey in a small bowl, then pour the mixture over the sprouts in the skillet.
Slice the rested chicken into strips and return it to the pan, tossing everything together to coat in the glaze.
Plate the chicken and sprouts immediately and garnish with the toasted walnuts.