Preheat your oven to 375°F (190°C) and line a large heavy-duty rimmed baking sheet with parchment paper.
In a small bowl, whisk together the olive oil, dried rosemary, dried thyme, garlic powder, sea salt, and black pepper to create a concentrated herb rub.
Pat the chicken breasts dry with a paper towel and rub half of the herb mixture thoroughly over all sides of the meat; let sit for 15 minutes to marinate.
While the chicken marinates, trim the Brussels sprouts and halve them, peel and slice the carrots into coins, and cut the red onion into uniform wedges.
Place the prepared vegetables in a large mixing bowl and toss with the remaining herb mixture until every piece is glistening and well-seasoned.
Arrange the chicken and vegetables in a single layer on the baking sheet, ensuring they are not overcrowded to allow for proper browning.
Bake for 35 to 40 minutes, rotating the pan halfway through, until the chicken is golden and the vegetables are caramelized and tender.
Whisk the balsamic vinegar and lemon juice together, then drizzle over the pan immediately before serving to add a sophisticated, acidic punch.