Place ham in a roasting pan and allow it to rest at room temperature for 30 to 45 minutes.
Preheat oven to 300 degrees F (150 degrees C).
Mix apple cider, orange juice, and vinegar together in a bowl.
Open the spirals of the ham to reveal more of the meat's surface area. Pour the juice mixture over the ham. Cover with aluminum foil.
Bake in the preheated oven until heated through, about 45 minutes.
Whisk maple syrup, dark brown sugar, white sugar, mustard, soy sauce, cinnamon, ginger, nutmeg, red pepper flakes, and cloves together in a saucepan over medium heat until shimmering and smooth, about 2 minutes. Simmer 2 minutes more; remove glaze from heat to cool a bit.
Increase oven temperature to 400 degrees F (200 degrees C).
Remove aluminum foil from heated ham. Brush 1/3 the glaze atop the ham to cover it completely.
Return ham to the hot oven. Bake, uncovered, about 8 minutes. Repeat adding glaze and baking for 8 minutes more.
Remove ham and baste a third time with remaining 1/3 glaze. Continue baking until glaze is caramelized and bubbly, 10 to 12 minutes. Remove from the oven and let rest 10 to 15 minutes before slicing. Drizzle pan juices on top.