How to Make It
Preheat a gas grill to medium-high (400°F to 450°F). Stir together thyme, allspice, cayenne, ginger, 1 tablespoon of the oil, and 1/2 teaspoon of the salt in a large bowl until combined. Add drumsticks; toss to coat.
Place chicken on lightly oiled grill grates; grill, covered, turning occasionally, until charred and a thermometer inserted in thickest portion registers 165°F, 16 to 18 minutes. (Alternative cooking method: Preheat oven to 475°F. Place a wire rack on a rimmed baking sheet lined with aluminum foil. Place chicken on rack. Bake in preheated oven until a thermometer inserted in thickest portion registers 165°F, about 18 minutes.)
While chicken cooks, whisk together lime juice, honey, and remaining 1 tablespoon oil and 1/2 teaspoon salt in a large bowl. Add mangos, jicama, cabbage, and scallions; toss to coat. Serve chicken with slaw.