Line a tray or baking sheet with parchment paper. To make the burgers, put the ground turkey in a large bowl. Squeeze out all the moisture of the shredded zucchini in paper towels. Add the zucchini, onion, garlic, paprika, salt, pepper, and crushed red pepper flakes to the turkey. Mix until combined, but don’t over mix. Form the mixture into four 1/2-inch-thick patties.
Place the patties in a single layer on the prepared tray or baking sheet. Put the burger patties in the freezer for 20 to 30 minutes. Freezing the patties will prevent them from falling apart on the grill.
While the patties are chilling, make the slaw. In a large bowl, combine the cabbage, cilantro, green onions, and jalapeño.
In a small bowl, whisk together the apple cider vinegar, olive oil, lime juice, honey, and Dijon mustard. Season with salt and pepper, to taste. Pour the dressing over the slaw and toss well. Set aside and let marinate while you make the burgers.
Preheat the grill to medium heat and brush with oil. Grill the burgers until cooked through, about 5 minutes per side, melting the cheese on top of the burgers during the last minute. A turkey burger is fully cooked when the center of the patty reaches an internal temperature of 165° F.
Place the burgers on the toasted buns and top with slaw. Serve immediately.