Preheat your oven to 400°F and line a large baking sheet with parchment paper for easy cleanup.
Trim and halve the Brussels sprouts and peel the carrots before cutting them into 1-inch pieces on a bias.
Toss the vegetables on the baking sheet with half of the olive oil and a pinch of sea salt and black pepper.
Roast the vegetables for 30 minutes, tossing halfway through, until they are tender and have developed caramelized edges.
While the vegetables roast, finely mince the garlic clove and the fresh thyme and rosemary leaves.
Season the chicken breast generously on both sides with the remaining sea salt and black pepper.
Heat the remaining olive oil in a heavy-bottomed oven-safe skillet over medium-high heat until shimmering.
Sear the chicken for 4 minutes until a deep golden crust forms, then flip the breast over.
Transfer the skillet directly into the oven and roast for 10-12 minutes until the internal temperature reaches 165°F.
Remove the chicken from the skillet and place it on a warm plate, tenting with foil to rest for 8 minutes.
Place the skillet back on the stovetop over medium heat, add the ghee, and sauté the garlic and herbs until fragrant.
Pour in the chicken bone broth and scrape the bottom of the pan to release the flavorful browned bits.
Simmer the sauce for 5 minutes until it reduces into a glossy glaze, then whisk the honey and balsamic together in a small bowl.
Drizzle the honey-balsamic mixture over the roasted vegetables and serve alongside the chicken topped with the herb pan sauce.