Trim the leaves away from the radishes. Leave a little bit of stem to use as a handle for dipping. It's nice for color as well.
Bring a small pot of water to a boil. Fill a medium-sized bowl with ice water.
Place the radish greens in the boiling water and blanch for 15-30 seconds, just until they turn a very bright green. Then immediately put them in the ice water. It's best to do this in a few batches so you can ensure great color on all the leaves without overcooking them.
Place the radish leaves in a kitchen towel and wring out as much water as possible.
Add the radish leaves, butter, and a pinch of sea salt to a small food processor. Pulse until the radish leaves are well-incorporated into the butter. Transfer the radish leaf butter to a serving dish, top the radishes with some good sea salt such as Maldon and serve!
Notes
Wash radishes thoroughly: Radishes and their leaves grow low to the ground so they can be very sandy. Wash them well under cold water, then give them a spin in the salad spinner, or allow to dry on a kitchen towel.
Storing radishes: I usually store them in the salad spinner covered in a damp paper towel until ready to use. You can also store them in a zip top bag with a damp paper towel. Don't close the bag all the way and place it in the crisper drawer.
Eat your radishes and their leaves quickly: Try to use your radishes within a few days of purchase, especially if you plan to eat the leaves. They are best when they are super fresh!
I think you really need a mini-food processor for this recipe, not a full sized one. There just isn't enough stuff for a big one. Perhaps a large one would work if you were doubling the recipe.
This recipe is adapted from Drinking French by David Lebovitz. I highly recommend it if you'd like to learn more about traditional French cocktails, aperitifs, and café drinks. It's a fascinating and well-researched book.
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