Combine turkey, egg, basil, breadcrumbs, salt and pepper. Mix gently. Make 12 balls. Flatten and place a slice of cheese on top of 6 burgers. Top with remaining burgers and pinch edges to seal cheese inside.
Sauté or grill burgers.
Cut ciabatta loaf into 6 squares. Slice each square open horizontally. Top with burger, tomatoes and avocado.