Place the chicken drumsticks into a large mixing bowl. Add the six cloves of minced garlic, the zest and juice of one lemon, za'atar, parsley, salt, and extra virgin olive oil to the bowl. With bare clean hands, rub the mixtures over the chicken drumsticks until evenly coated. Cover, and place in the fridge for at least two hours, or up to eight.
When it's go time, preheat the grill to to about 425º F. Lightly brush the grates with a bit of olive oil. Place the chicken drumsticks onto the grates and grill them for about 20 minutes or until they reach an internal temperature of 165º F, rotate them on the grill every 5 minutes.
Once the drumsticks are nicely crisped and ready to eat, remove them from the grill and set them on a plate. Let them stand for five minutes before eating. Garnish with freshly chopped parsley and/or mint, and serve with the lemon yogurt sauce.