Begin by seasoning the chicken breast with sea salt and black pepper, then let it rest at room temperature for 30 minutes to dry-brine for a more succulent texture.
Preheat your oven to 400°F.
Prepare the gourmet vegetables by halving the Brussels sprouts, peeling and cubing the parsnips into 1/2-inch pieces, and finely mincing the shallots, garlic, and fresh herbs.
Toss the Brussels sprouts and parsnips with 0.5 tbsp of olive oil on a large baking sheet and roast for 30 minutes until deeply caramelized and tender.
Heat the remaining 0.25 tbsp of olive oil in a heavy-bottomed, oven-safe skillet over medium-high heat.
Sear the chicken for 4 minutes per side until a golden-brown crust forms.
Transfer the skillet to the oven for 8-10 minutes until the internal temperature of the chicken reaches 165°F, then remove and let rest on a cutting board for 5 minutes.
In the same skillet over medium-low heat, sauté the minced shallots and garlic for 3 minutes until translucent and fragrant.
Stir in the fresh thyme, rosemary, and balsamic vinegar, simmering for 3-4 minutes while scraping the pan to create a thick, glossy reduction.
Slice the chicken against the grain and serve alongside the roasted vegetables, drizzling the warm balsamic-herb sauce over the entire plate.