Rinse the radishes thoroughly under cool running water to remove any dirt. Trim the green tops with kitchen shears and dry completely.

Slice the radishes thinly to about 1/8-inch thickness, ensuring uniform slices.

In a bowl, whisk together lemon juice and olive oil until emulsified, about 30 seconds.

Add the sliced radishes to the bowl and gently toss to coat them evenly with dressing.

Sprinkle Parmesan cheese and dill over the salad, and season with salt and pepper before tossing gently.

Plate the salad in a single layer on a serving plate, garnishing with extra Parmesan and dill if desired.