To make the dressing, combine all ingredients using an immersion blender or food processor and blend until smooth. Taste and add more salt, acid, or sweetener if needed.

Wash radishes well, trim and top, then slice thinly with a mandolin. Lay each slice carefully, trying to cover just half of each radish slice with the next.

Gently spoon dressing over sliced radishes and cover the plate with plastic wrap, avoiding contact with the carpaccio. Refrigerate until ready to serve (up to 3 hours). Serve cold.

The dressing can be stored in an airtight jar in the refrigerator for up to 2 weeks. Herbs will settle to the bottom as they sit. Shake well before serving. When the dressing has been stored in the refrigerator for a while, it may thicken. Let it come to room temperature before serving.