Preheat the oven to 350 degrees F. Line the bottom and the rack of a roasting pan with foil. Place the rack inside the roasting pan.
With the fatty side facing down, use a sharp knife to cut 3/4-inch long diagonal lines about 1-inch deep all over the surface of the ham. Working in the opposite direction, cut more 3/4-inch long and 1-inch deep diagonal lines to create diamond shapes. Turn the ham over so the fatty side is facing up. Create the same diamond shape placing any pieces of ham that fall off back onto the ham. Place the ham, fatty-side up, on the rack and cook, rotating the pan halfway through, until warm in the center and the fat starts to crisp up, about 2 hours.
Meanwhile, mix 3 cups sugar, 3/4 cup orange juice, 1/2 teaspoon cayenne pepper, 1 tablespoon salt and 1 teaspoon pepper in a medium bowl. Remove the ham from the oven and carefully brush one-third of the glaze all over the ham. Bake the ham for 20 minutes. Brush with another third of the glaze and bake for 20 minutes more. Brush the remaining third of the glaze over the ham and cook until the glaze is shiny and the skin is dark golden brown and crispy, about 30 minutes more.
Mix the remaining 1/2 cup sugar, 1 cup orange juice, 1/2 teaspoon cayenne pepper and a generous amount of pepper in a small saucepan and bring to a boil over medium-high heat. Cook, stirring frequently, until the sugar is dissolved and the sauce has reduced by about half, 7 to 8 minutes. Remove the ham from the oven and let rest for 15 minutes. Transfer to a cutting board. Slice and serve with the sauce on the side.
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