Preheat your oven to 220°C (430°F).
Pat the lamb roast dry with paper towels, then generously season all over with salt and pepper. Drizzle with olive oil and rub it into the meat for even coverage.
Heat a skillet over high heat until shimmering, then place the lamb in the pan. Sear on all sides until deep golden brown, about 4 minutes per side, listening for a satisfying sizzle and watching for a rich color developing.
Transfer the seared lamb to a roasting pan, tuck crushed garlic cloves and rosemary sprigs around it for aromatic flavor.
Roast in the oven at 220°C for 15 minutes to start browning, then lower the temperature to 160°C (320°F) and continue roasting for about 1.5 hours, or until a meat thermometer inserted into the thickest part reads 60°C (140°F) for medium rare, with juices running clear.
Halfway through cooking, baste the lamb with the pan juices to keep it moist and flavorful, using a spoon to spoon the juices over the top.
While the lamb roasts, toss the chopped carrots and potatoes with a little olive oil, salt, and pepper. Arrange them on a baking sheet and roast alongside the lamb during the last 45 minutes for tender, caramelized vegetables.
Once the lamb reaches desired doneness, remove it from the oven and transfer to a cutting board. Tent loosely with foil and let rest for at least 20 minutes — this helps the juices redistribute and keeps the meat juicy.
Meanwhile, pour the pan drippings into a skillet over medium heat, add red wine or broth, and scrape up any browned bits. Simmer until slightly reduced and flavorful, creating a smoky, rich sauce.
Carve the rested lamb into slices, revealing a juicy, rosy interior with a crispy crust.
Serve the sliced lamb with roasted vegetables, drizzled with the pan sauce for a warm, hearty Christmas dinner.