Preheat oven to 375 degrees F.
Pat dry meat with paper towels. Season the lamb legs with salt and pepper on both sides. Place on a chopping board and gently cut halfway down into the leg to make an incision so the meat opens out, creating a pocket.
Mix all the stuffing ingredients in a bowl.
Mix all the sauce ingredients in a bowl.
Lightly grease with olive oil a 9x13 inch baking dish.
Scoop the stuffing into the created pockets and secure the opening with toothpicks.
Transfer the legs of lamb into the prepared baking dish and top with the sauce mixture.
Add whole garlic and carrots to the baking dish, distributing evenly. Add 3 sprigs of rosemary.
Roast for about an hour and a half, basting the lamb after 30 minutes and every 15 minutes after that until the meat is cooked and golden brown.
Once cooked, discard rosemary and garnish the dish with remaining fresh rosemary sprigs and chopped parsley. Let the meat rest for 15 minutes before serving.