In small bowl stir together mayonnaise and pesto.
To assemble wrap: Over one wrap spread heaping Tbsp mayonnaise mixture. Place 3oz turkey down center of wrap. Top with 4 slices cheese, 4 basil leaves, 1/4 of the tomatoes and 1/2 cup greens. Drizzle with vinegar.
Starting on one side, roll up; cut in half. Repeat with remaining wraps and ingredients.