Process mayonnaise, sour cream, tahini, lemon juice, and anchovies in a food processor until anchovies are finely chopped, about 1 minute. Add basil, parsley, cilantro, scallions, dill, salt, and pepper; process until smooth and light green in color, about 1 minute. Transfer dressing to a bowl. Cover and refrigerate until well chilled, about 20 minutes.
Arrange lettuce wedges on one or two serving platters. Spoon 1 cup dressing evenly over cut sides of wedges. Top with cucumbers and radishes. Garnish with sesame seeds, additional cilantro and dill, and salt and pepper to taste. Serve with remaining dressing.
