Rinse the ham under cool running water and blot dry with paper towels. Let sit at room temperature for 2 hours. Move the oven rack to the lowest level. Preheat oven to 250 F. Line a roasting pan with aluminum foil and set a roasting rack inside it. Place the ham on the rack with the thinner rind on the bottom. Pour 1/2 cup of the apple cider over it, and cook for 2 hours, or until an instant-read thermometer registers 140 degrees.

Heat a heavy skillet over medium-low heat, and toast the mustard seeds, cardamom, and fennel, stirring frequently, until fragrant, about 3-4 minutes. Coarsely gind the toasted spices with a mortar and pestle or spice mill, then transfer to a medium bowl. Stir in the cinnamon, ginger, mustard, 2 tablespooons of the light brown sugar, 2 tablespoons of the dark brown sugar, the corn syrup, molasses, and last 1/2 cup of apple cider. Stir until well-incorporated, and set aside. 

Allow the ham to cool for 30 minutes. When cool enough to handle, use a sharp knife to trim off the hard rind, then trim the fat to roughly 1/4 inch thick all over. Set the ham, bottom side up, directly in the pan. Use the knife to score the fat on top of the ham with 1- or 2-inch large diamonds, slicing 1/4-1/2 inch through the fat into the meat. Poke a whole clove into the intersection where each diamond meets. Use your fingers to rub the spice glaze all over the ham, making sure a generous amount goes into the slices. 

In a medium bowl, stir together the last cup of light brown sugar and last 1/2 cup and 2 tablespoons of dark brown sugar. Use your hands to gently pack the sugar mixture all over the scored fat. Return the ham to the oven and bake for an additional 20 minutes. Use a brush and the last of the apple cider glaze to gently baste areas where the sugar is still hard. Cook for 40 more minutes, basting with more glaze (not pan juices!) after 20 minutes. Cook until the ham has a dark brown crust, an additional 15 minutes if necessary. Transfer to a serving platter and let rest for 30 minutes before carving.