Put the ham in a large roasting pan, fat side up. Using a sharp knife, score the ham with cuts across the skin, about 2-inches apart and 1/2-inch deep. Cut diagonally down the slashes to form a diamond pattern; season the meat generously with salt and pepper. Chop about 8 of the sage leaves and put in a bowl; mix with the oil to make a paste. Rub the sage-oil all over the ham, being sure to get the flavor into all the slits. Bake the ham for 2 hours. Now there is plenty of time to bang-out the orange glaze.
For the glaze: Place a saucepan over medium heat. Add the chunks of butter, oranges, orange juice, brown sugar, water, and spices. Slowly cook the liquid down to a syrupy glaze; this should take about 30 to 40 minutes.
After the ham has been going for a couple of hours, pour the orange glaze all over it, with the pieces of fruit and all. Scatter the remaining sage leaves on top and stick the ham back in the oven. Continue to cook for 1 1/2 hours, basting with the juices every 30 minutes.
Scatter the carrots around the ham and coat in the orange glaze. Stick the ham once again back in the oven and cook for a final 30 minutes, until the carrots are tender, the ham is dark and crispy, and the whole thing is glistening with a sugary glaze.
Set the ham on a cutting board to rest before carving. Serve the carrots and orange glaze on the side.