In a small bowl, combine the mint, rosemary and garlic. Open up the lamb flat on a baking sheet and top with some salt and pepper, about 2 tablespoons of the honey and about three-quarters of the herb-garlic mix. Roll up the lamb and tie it with butcher's twine, then top with the remaining honey and herb-garlic mix. Refrigerate, uncovered, for about 2 hours to marinate, then let the lamb come to room temperature before cooking.
Preheat the oven to 325 degrees F.
Add the chicken broth, white wine, carrots, onions and fennel to a large Dutch oven, then set the lamb on top of the vegetables. Roast until the lamb registers an internal temperature of 130 degrees F (medium rare) on an instant-read thermometer, about 2 hours.
Let the lamb rest on a cutting board for 15 minutes. Using a slotted spoon, transfer the vegetables to a serving platter.
In a small bowl, use a fork to mash the butter and flour together to form a smooth paste. Place the Dutch oven with the pan juices over medium heat and bring to a simmer, then whisk in the butter and flour mixture. Bring to a boil and heat until thickened, about 3 minutes.
Slice the lamb and serve with the vegetables and pan sauce spooned over.