Heat the oven to 325 degrees F.
In a bowl, mix together the brown sugar, honey, orange zest, 1/4 cup orange juice, pumpkin pie spice, and nutmeg. Season with salt.
Roll out enough aluminum foil to surround the ham and place the ham in the center of the foil. Peel back the layers of the ham and place a sprig of thyme between every other layer of the spirals. Pour half of the glaze over the ham allowing it to sink into the slices. Tightly wrap the ham in the foil and place on a rack in a roasting pan. Fill the pan with an inch of water and roast in the oven until the internal temperature reaches 140 degrees F, about 20 minutes per pound.
Pour the remaining half of the glaze in a small saucepot on medium heat and bring to a simmer. Whisk until small bubbles appear all over, then turn off the heat. The glaze will thicken as it rests.
Raise the oven temperature to 400 degrees F.
Remove the ham from the oven. Using caution and tongs to help, peel back the aluminum foil from the top, leaving the aluminum foil on the sides and underneath the ham to catch the glaze and juices. Slather the remaining glaze all over the top of the ham and place back in the oven uncovered for 15 more minutes. Remove and let rest before slicing.