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1
Make the Pork Preheat the oven to 350.
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2
Arrange the garlic cut side up on a sheet of foil, drizzle with oil and season with salt and pepper.
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3
Wrap the garlic in the foil and roast for about 1 hour, until very soft.
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4
Let cool, then squeeze the garlic cloves out of the skins into a medium bowl.
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5
Add the thyme, mustard powder, paprika, ginger, orange zest and the 1/4 cup of oil and mash into a paste.
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6
Reduce the oven temperature to 300.
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7
Set a rack in a flameproof medium roasting pan and put the pork on it.
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8
Season the pork with salt and pepper, then rub it all over with the garlic paste.
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9
Cover with foil and roast for 6 hours, until an instant-read thermometer inserted in the thickest part of the meat registers 200; uncover for the last 45 minutes of cooking.
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10
Transfer to a work surface and let cool, then shred.
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11
Discard the fat and bones.
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12
Spoon off all but 2 tablespoons of fat from the roasting pan.
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13
Add the sugar, both vinegars and 1/2 cup of water to the pan and cook over moderately high heat, whisking, until bubbling and the sugar dissolves, 5 minutes.
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14
Add the pork and toss to coat.
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15
Season the pork generously with salt and pepper and toss again; keep warm.
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16
Meanwhile, make the Sauce In a saucepan, whisk the ketchup, cola, vinegar, hot sauce, molasses and cornstarch and bring to a boil.
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17
Simmer over moderate heat, stirring, until glossy and thick, 8 minutes; keep warm.
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18
Pile the pork on the buns and top with the barbecue sauce and coleslaw.
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19
Close the sandwiches and serve, passing the habanero vinegar at the table.
