Late March to May is the peak season for shin-tamanegi (new-harvest onions). Unlike the usual yellow variety, these large, white bulbs have not been aged, making them less sharp and with plenty of sweetness.
Shin-tamanegi can be used in the same way as yellow onions, but I prefer to take full advantage of their crunchiness and sweetness in salads and other raw dishes. If they are sliced thinly and soaked in water for a little while, they have almost no sharpness and a really nice texture.
These onions are of course delicious when cooked — try boiling a whole one in soup or dashi stock until it becomes meltingly tender — but eating them raw also allows you to take full advantage of the diallyl sulfide present in onions. Although this is the substance that makes your eyes tear up, diallyl sulfide also stimulates your digestive system.