Preheat your oven to 400°F (200°C).
Trim any excess fat from the lamb loin chops and pat them completely dry with a paper towel.
Toss the halved Brussels sprouts and sliced carrots with 0.25 tablespoons of the olive oil on a large rimmed baking sheet.
Roast the vegetables for 20 to 25 minutes until they are tender and beautifully caramelized.
In a small bowl, mix together the dried rosemary, thyme, garlic powder, sea salt, and black pepper.
Press the herb seasoning mixture firmly onto both sides of each lamb chop to create a thick crust.
Heat the remaining 0.25 tablespoons of olive oil in a cast-iron skillet over medium-high heat until shimmering.
Sear the lamb chops for 3 to 4 minutes per side for medium-rare, or until your preferred level of doneness is reached.
Transfer the lamb to a plate and let it rest for 5 minutes before serving with the roasted vegetables.