In a glass or ceramic bowl, combine chicken pieces with minced garlic, thyme leaves, cumin if using, salt and pepper.
Use your hands to massage the seasonings into the meat for 15-20 seconds, coating each piece evenly.
Pour fresh lemon juice over the chicken to begin the tenderizing process.
Drizzle olive oil over everything to carry fat-soluble flavors into the meat.
Cover tightly with plastic wrap and refrigerate for 12-24 hours.
If using wooden skewers, soak them in water for 30 minutes to prevent burning.
Thread chicken pieces onto skewers, alternating with vegetables if desired.
Bring your grill or broiler to medium-high heat (375°F/190°C).
Cook skewers for 5-6 minutes per side, turning only once.
Reserve a tablespoon of marinade and brush onto skewers during the final minute of cooking.
