Preheat oven to 180°C. Use a small sharp knife to cut a zig-zag around the neck of the ham, then prise away the skin using fingers. Arrange in a roasting pan.
Combine the barbecue sauce, marmalade, brown sugar, bourbon, spices and mint in a medium saucepan and boil for 10 minutes, until thickened. Brush a little glaze onto the ham, then bake for 20 minutes. Continue baking and basting for 1 more hour, until glossy.
Halve the potatoes, then cut fine parallel lines on the curved side. Toss in olive oil, season with salt and pepper, then arrange flat side down in a lined oven tray. Bake for 1½ hours, until golden and crisp. Carve the ham and serve with the potatoes, gravy, greens and cornbread.