Start by making the dressing. Place all ingredients except for the oil into a food processor. With the motor running, drizzle in the oil slowly so it can properly emulsify. Taste and adjust seasoning. Store in an airtight container for up to 3 days.
Next, slice all the radishes into thin rounds, as thin as you can. If not using immediately, store submerged in cold water in a bowl to keep them crisp and prevent them from drying out. You can actually keep them like this overnight if needed.
Toss all the ingredients together in a bowl, making sure not to overdo it on the dressing. I would recommend using 2 tablespoons of the dressing to start and adding more if needed. The butter lettuce is extremely thin and will wilt easily if too much dressing is used. Serve on individual plates or in a large serving bowl.