Prep the Grill: Preheat your grill to medium-high heat. Lightly spray the grill grates with cooking spray to prevent sticking.
Make the Dry Rub: In a small bowl, combine the cumin, chili powder, sea salt, cayenne pepper, and mustard powder. Rub the mixture evenly on both sides of the chicken thighs.
Prepare the Glaze:In a medium saucepan, combine the apple juice and honey. Bring to a boil, then reduce the heat and simmer until the mixture is reduced by half, about 10 minutes.
In a small bowl, mix the cornstarch with water until smooth. Whisk the cornstarch mixture into the reduced juice and continue to boil for 1–2 minutes, whisking constantly, until the glaze thickens.
Remove the glaze from the heat and stir in the grated lime rind, fresh lime juice, and cayenne pepper. Pour half of the glaze into a separate bowl for basting.
Grill the Chicken:Place the chicken directly over the heat and grill for 5 minutes on each side, basting occasionally with the glaze.
Move the chicken to indirect heat (or turn off half of the burners on a gas grill) and continue grilling for another 5 minutes per side, or until the internal temperature reaches 165°F (74°C). Baste occasionally with the remaining glaze.
Serve: Transfer the chicken to a platter and serve with extra glaze. Pairs wonderfully with rice pilaf, roasted vegetables, or a fresh salad.