Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper.
Slice the carrot into 1/2-inch thick rounds and place them on the baking sheet with the broccoli florets.
Drizzle the vegetables with 0.5 tbsp of olive oil and season with a pinch of the sea salt and black pepper; toss to coat and spread in a single layer.
Roast the vegetables in the oven for 18-20 minutes, or until they are tender and the edges are slightly caramelized.
While the vegetables roast, mince the garlic and finely chop the fresh rosemary and thyme.
In a small bowl, combine the minced garlic, rosemary, thyme, and the remaining sea salt and black pepper.
Pat the lamb chops dry with a paper towel and rub the herb mixture firmly onto both sides of each chop.
Heat the remaining 0.5 tbsp of olive oil in a heavy cast-iron skillet over medium-high heat until shimmering.
Place the lamb chops in the skillet and sear for 3 to 4 minutes per side for medium-rare, or until the internal temperature reaches 145°F.
Remove the lamb from the skillet and let it rest on a plate for 5 minutes to allow the juices to redistribute.
Plate the herb-crusted lamb chops alongside the roasted broccoli and carrots and serve immediately.