Preheat your oven to 400°F (200°C).
Halve the baby potatoes and slice the carrots into thick coins.
Toss the potatoes and carrots with half of the olive oil, minced garlic, sea salt, pepper, and fresh rosemary sprigs on a baking sheet.
Roast the vegetables for 20 minutes.
Slice the zucchini into rounds and add them to the baking sheet, tossing with the other vegetables, and roast for an additional 10-12 minutes until tender.
While vegetables finish roasting, season the mutton chops generously with salt and pepper.
Heat the remaining olive oil in a cast-iron skillet over medium-high heat.
Sear the mutton chops for 4 to 5 minutes per side for medium-rare, or until they reach your preferred level of doneness.
Remove the chops from the pan and let them rest for 5 minutes to lock in the juices.
Serve the seared mutton chops alongside the herb-roasted vegetables and enjoy immediately.