For the Carolina Slaw:
Assemble the vegetables on a cutting board or in a large bowl. Working in batches, transfer a few cups of the vegetable combination to a food processor at a time and pulse 3-4 times to a rice-like consistency. You want the slaw to be fine enough to hold together on a slider bun, but be careful not to over-process. Transfer all the processed vegetables to a large bowl.
In a small bowl or measuring cup, stir together the remaining ingredients and pour over the processed vegetables.
Cover and refrigerate until ready to serve. The slaw can be made a day ahead.
For the Tarheel Sliders:
Prepare a sheet pan lined with parchment or waxed paper.
Put the ground beef in a large bowl and sprinkle the Tarheel BBQ Rub over the top. Gently knead the spice into the meat and divide into 12 equal portions. Roll each portion into a ball and flatten into a 4" patty. Line up the prepared patties on the sheet pan.
Preheat your grill to high heat. Grill the patties about 6 minutes total, flipping once or twice during the cooking time.
Serve immediately on slider buns with Carolina slaw, ketchup and a pickle.
Notes:
Slaw recipe adapted from Bon Appétit: Carolina Cole Slaw