For the pulled pork slider: Marinate the pork in the orange juice, lemon juice and garlic in a baking dish in the refrigerator overnight.
Preheat the oven to 280 degrees F. Remove the pork from the marinade, transfer to a baking dish and cover with foil. Roast until tender and falling apart, about 4 hours. Let cool until cool enough to handle. Shred the meat with 2 forks.
Heat the shredded pork with the barbecue sauce in a saucepan over low heat until warmed through.
For the green cabbage slaw: Toss the cabbage with the vinegar, sugar and salt in a medium bowl. Let sit for 20 minutes in the refrigerator.
Toast the bun with the butter. Make a sandwich with the bun, pulled pork mixture, green cabbage slaw and basil.
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