Preheat the oven to 325°F. Remove the skin from the top of the ham and score the fat in a criss-cross pattern, making sure to only cut through the fat and not the meat. Place in a large roasting pan.
Combine ¼ cup apricot jam, ¼ cup bourbon, ¼ cup brown sugar, and 2 Tbsp Dijon mustard in a small mixing bowl and whisk until combined. There will likely still be lumps of jam, but that's okay- they will melt in the oven.
Brush the mixture all over the top and sides of the ham. Cover with a lid or aluminum foil. Bake for 12-15 minutes per pound of meat, but plan to remove the ham from the oven about 15 minutes before it's finished baking.
While the ham is in the oven, make your glaze. In a medium-sized saucepan, combine ⅓ cup brown sugar, ¼ cup apricot jam, ½ cup bourbon, 2 tsp cornstarch, and 2 Tbsp Dijon mustard and whisk until combined. Turn the stove on medium-high and bring to a boil. Boil for another couple of minutes until the sauce has thickened, then turn off the heat and leave the saucepan on the hot burner. Taste to see if you think it needs a pinch of salt (optional)- if so, add now.
Once the ham is nearly finished cooking and only has 15 more minutes to go, remove it from the oven and take the lid or foil off. Brush the top and sides of the ham with your glaze, pouring any excess over the top of the ham.
Return to the oven for the remaining time, or until the glaze has nicely browned on top. Remove from the oven and let rest for 20 minutes before carving or slicing.