Trim the root and all but one inch of the green from the leeks. Cut them in half lengthwise, and wash out any lingering dirt. Slice the leeks thinly, about 1/8-inch thick.

Separate the cloves of garlic. Hit each with the side of a knife, just enough to smash a wee bit, so the paper is easily removed. Mince or press through a garlic press.

Cut the potatoes in chunks, about ¾ -inch.

Heat the olive oil in a pressure cooker or soup pot. Add the leeks and sauté on medium flame about 5 minutes. Add the garlic; cook and stir a few more minutes.

Pour the vegetable broth over the garlic and leeks. Add the potatoes and parsley.

For pressure cooking, bring to pressure and cook 5 minutes. Remove from the heat and allow the pressure to come down naturally for another 5 minutes. Then release the remaining pressure by running under cold water.

Without a pressure cooker, cover the soup and cook at least ½ hour, until the potatoes are very soft.

Puree with an immersion blender or carefully in batches in the blender. (Beware hot liquids in a blender have the urge to get out and burn the nearest victim, so only fill the blender half full each batch.) Return the blended soup to a pot.

Serve hot, garnished with parsley. Float an egg, fried over easy, in each bowl of soup, if desired.