Preheat your oven to 400°F (200°C).
On a large rimmed baking sheet, toss the broccoli florets and sliced carrots with half of the olive oil, a pinch of sea salt, and black pepper.
Spread the vegetables in a single layer and roast for 20 minutes until they are tender and the edges are slightly caramelized.
While the vegetables roast, season the chicken breast on both sides with the dried oregano, garlic powder, lemon zest, and the remaining salt and pepper.
Heat the remaining olive oil in a cast-iron or heavy-bottomed skillet over medium-high heat.
Place the chicken in the skillet and sear for 5-7 minutes per side, or until the exterior is golden-brown and the internal temperature reaches 165°F.
Remove the chicken from the heat and drizzle with fresh lemon juice while it rests for 2 minutes.
Plate the crispy chicken alongside the roasted vegetables and serve immediately.