1. To prepare dressing, combine first 9 ingredients in a small food processor or blender; process 30 seconds or until pureed, scraping sides of bowl occasionally. Cover and chill.
2. To prepare salad, slice each tomato crosswise into 4 equal slices (about ½ inch thick). Place 1 tomato slice on each of 4 salad plates; sprinkle slice evenly with ¼ teaspoon salt. Top each serving with a few onion pieces and about 1 tablespoon avocado. Repeat layers 3 times, ending with avocado. Drizzle 2 tablespoons dressing over each serving; sprinkle with black pepper, if desired.