Using hands mix the lamb, onion and garlic thoroughly. Mix in the cinnamon, all spice, breadcrumbs and pepper and shape the mixture around the satay sticks, leaving about half the stick uncovered. Brush lightly with olive oil.
Grill the koftas until cooked as preferred.
To make the Basil Butter, mix together all ingredients until well blended.
Spread prepared Basil Butter onto lightly warmed pita bread, wrap around the koftas and serve with Tabouleh.