Preheat your oven to 400°F (200°C).
On a large baking sheet, toss the broccoli florets and sliced carrots with half of the olive oil, a pinch of sea salt, and a pinch of black pepper.
Roast the vegetables in the oven for 15 to 20 minutes until they are tender and slightly charred at the edges.
While the vegetables roast, whisk together the honey, tamari, minced garlic, and grated ginger in a small bowl to create the glaze.
Season the chicken breast with the remaining sea salt and black pepper.
Heat the remaining olive oil in a skillet over medium-high heat and sear the chicken for about 5 to 6 minutes per side until cooked through.
Reduce the heat to low and pour the honey-garlic glaze into the skillet, basting the chicken continuously for 1 to 2 minutes until the sauce becomes thick and glossy.
Plate the glazed chicken alongside the roasted vegetables and drizzle any remaining sauce from the pan over the top.