To make the dressing. Combine all ingredients in a bowl or glass jar. Taste and adjust the salt and pepper.To make the wraps. In a large salad bowl, combine the lettuce, avocado, and basil. Toss with 1/2 of the dressing. Place one tortilla at a time in the microwave for 20 seconds. Spread on a layer of pesto, then add the salad, chicken, bacon, and cheese. Drizzle over more dressing. Fold the tortilla over the ingredients. Fold sides and ends of tortillas over filling and roll forward. Repeat with remaining ingredients.Serve room temp or place in a skillet with olive oil to warm. Enjoy with extra dressing and pesto.