In a food processor, combine avocado cubes, lemon or lime juice, basil, tarragon, garlic, and asorbic acid. Blend until smooth. With the motor running, slowly pour in olive oil to make a thick, creamy dressing. If dressing is too thick to pour, add water, a few tablespoons at a time, to reach the desired consistency. Pour into a bowl, season, to taste, with salt and pepper and cover. Refrigerate until chilled.