Fill a saucepan with 2-3 inches of water and bring to a moderate simmer. Crack each egg into its own individual cup and add the egg all at once to the simmering water. Add the other egg. Simmer for 3-5 minutes, depending on the desired doneness.
Prepare a bed of arugula on each plate and add the shaved radish. Toss with a light lemon vinaigrette or any other favorite dressing.