Prepare the Meatballs: In a bowl, combine the ground meat, smoked paprika, coriander, and salt. Roll into 1-inch balls (about 35 total).
Broil: Arrange the meatballs on a nonstick-foil-lined rimmed baking sheet. Broil until cooked through, about 6 to 8 minutes.
Fry the Slaw: Heat oil in a large skillet on medium-high. Fry the grated carrots and ginger in batches until crisp, about 3 to 5 minutes. Transfer to paper towels to drain, then toss with fresh cilantro.
Assemble: Prepare the sauce by mixing the Greek yogurt and harissa. Stuff the pita halves with meatballs and crispy carrot slaw, then drizzle with the harissa-yogurt sauce.