In a small bowl, mash together avocado, mayonnaise or sour cream, lime juice, salt, and pepper until smooth and creamy.
Lay the tortilla flat and spread the avocado mixture evenly across the surface, leaving about 1 inch border around edges.
Layer the turkey slices over the avocado spread.
Add leafy greens, shredded carrots, cherry tomatoes, and cucumber slices if using.
Starting from one edge, roll the tortilla tightly, tucking in the sides as you go.
Cut the wrap in half diagonally and serve immediately or wrap in foil for later.