Combine spinach, parsley, basil, chives, tarragon, shallot, garlic, anchovy paste, and lime juice in a high-powered blender; blend and slowly add oil through top opening of blender until mixture is smooth, about 1 minute, scraping down sides if needed. Add mayonnaise and salt; blend until smooth. Cover and chill until ready to serve.

Combine cabbage, romaine, cucumber, and scallions in a large bowl; add 2/3 cup of the dressing and toss to evenly coat. Divide between 4 bowls and top each bowl with avocado and 1 tablespoon of the pistachios. Serve immediately with remaining dressing.