Start by breading and frying the avocado. Slice the avocado in half, remove the pit, and then cut each half into four slices. Remove the slices from the skin and set aside. Then whisk the egg. One by one, dredge the avocado slices in the breadcrumbs, then coat with the egg, and dredge in the breadcrumbs again. Heat the olive oil in a small skillet over medium heat. Once hot, add the avocado, and toast each side for about 2 minutes, until golden brown.
While the avocado is frying, make the dressing. To make the dressing whisk together the yogurt, ginger, lemon juice, vinegar, and olive oil. Season with salt and pepper to taste. Pour a few tablespoons of the dressing over the shredded cabbage and carrots and toss to mix.
Assemble the wraps by dividing the fried avocado, chicken, cheese, and the cabbage and carrot mix between two wraps, and then roll them up and serve.