Slow-roasting the pork with liquid (a mix of ale and water) in the pan makes the meat fall-apart tender. A blast of heat at the end crisps the skin.
Combine 1/4 cup salt, sugar, ginger, cloves, and mustard powder in a small bowl.
Using a sharp knife, score skin (but not meat) on top and sides of pork in a diamond pattern at 1/2-inch intervals, leaving bone end unscored. Make about a dozen 1/2-inch-deep slits into flesh on top and underside using the tip of the knife. Transfer pork to a rimmed baking sheet or baking dish, and rub spice mixture into scored skin and flesh. Refrigerate, loosely covered with parchment, 12 to 24 hours.
Let pork stand at room temperature for 1 1/2 to 2 hours before roasting. Uncover.
Preheat oven to 325 degrees. Transfer pork to a clean rimmed baking sheet and pat skin dry. Pour beer and 1 1/2 cups water into baking sheet and wrap entire sheet in foil. Carefully transfer pork to oven and roast until meat is tender when pierced with a fork, about 3 hours and 15 minutes. Uncover pork.
Toss kumquats with honey. Add to baking sheet, turning to coat. Roast until tender and lightly caramelized, about 30 minutes.
Raise oven temperature to 425 degrees. Roast until pork skin is crisp and dark brown, 8 to 10 minutes. Let pork rest, tented with foil, for 45 minutes before carving. Serve with kumquats in pan juices.
Spice-rubbed pork can be refrigerated for up to 1 day. Bring to room temperature before roasting.