Cut red radishes into halves or quarters, if large; place in prepared ice bath with sliced watermelon radishes. Refrigerate until ready to use.
In the container of a blender, combine mayonnaise, cream, sour cream, parsley, tarragon, chives, lemon juice, anchovies, garlic, and pepper; purée until smooth and well combined, about 1 minute.
Drain radishes and pat dry; arrange on a serving platter with dressing. Garnish with tarragon, parsley, and chives, if desired.
Recipe by Southern Lady Magazine at https://southernladymagazine.com/mixed-radishes-green-goddess-dressing/