Preheat your oven to 400°F (200°C).
Peel and slice the carrots and parsnips into 1-inch thick rounds or chunks.
Toss the vegetables on a baking sheet with 1 teaspoon of olive oil, half of the sea salt, and half of the black pepper.
Roast the root vegetables for 25 minutes, flipping once halfway through, until they are tender and caramelized.
While the vegetables roast, finely mince the garlic, rosemary, and thyme, then mix them together in a small bowl.
Pat the lamb loin chops dry with a paper towel and brush all sides with the Dijon mustard.
Press the herb and garlic mixture firmly onto the mustard-coated lamb chops to create an even crust.
Heat the remaining 1 teaspoon of olive oil in a heavy, oven-safe skillet over medium-high heat.
Sear the lamb chops for 2 minutes per side to develop a golden crust, then transfer the skillet directly into the oven for 5 to 7 minutes for medium-rare.
Remove the lamb from the oven and let it rest for 5 minutes before serving alongside the roasted vegetables.