Mix together the yogurt, minced garlic, paprika, cumin, cayenne, salt, and black pepper in a large bowl until smooth and well combined.
Add the chicken drumsticks to the bowl and coat them thoroughly with the marinade, ensuring every piece is evenly covered.
Cover the bowl with plastic wrap and refrigerate overnight or at least for 4 hours to allow the flavors to penetrate and the meat to tenderize.
Preheat the grill to medium-high heat, aiming for around 375–400°F (190–200°C), until hot and slightly smoky.
Remove the chicken from the marinade, letting any excess drip off, and place the drumsticks directly on the grill grates, skin side down.
Grill the drumsticks for about 10–12 minutes on one side, until they develop a nice char and the skin begins to crisp up with visual grill marks.
Flip the drumsticks over and continue grilling for another 10–12 minutes, rotating occasionally, until they are cooked through and have an even golden-brown color.
Use a meat thermometer to check that the internal temperature reaches 165°F (74°C), ensuring the chicken is fully cooked and juicy inside.
Remove the chicken from the grill and let it rest for 5 minutes to allow the juices to settle.
Serve the grilled drumsticks hot, garnished with fresh herbs or lemon if desired, and enjoy the crispy, smoky exterior with tender meat inside.
