Peel and quarter the sweet potatoes.
Wash the leeks well, and drain. Remove any damaged outside peel, remove the hairy white tips from the end, and cut the leeks into 1-inch slices. Leave 1 (3-inch) section aside to be fried for the garnish. In a large pot, cook the leeks with the butter until soft. Do not brown. Add the stock or water.
Add the sweet potatoes, and bring to a boil. Reduce the heat to medium, and boil until cooked through, just softer than fork tender.
Using an immersion blender, puree the ingredients until they are thoroughly blended. Add the grated ginger, and test for consistency. If too thick, add a bit more water. Taste for seasoning, adding more salt or pepper, as needed. Ladle the soup into warm bowls, and garnish with a mound of hot crispy matchstick potatoes and frizzled leeks.
In a large heavy-bottomed saucepan, pour enough oil to fill the pan about a third of the way. Heat over medium heat until a deep-frying thermometer inserted in the oil reaches 350 degrees F. (If you don't have a thermometer, a cube of bread will brown in about 3 minutes.)
To make matchstick fries: Peel and cut potatoes into matchstick slices. Rinse them under cold water in a strainer to remove the excess starch. Let drain well, and pat dry. Fry for 3 to 5 minutes submerged in canola oil, until they are a nice deep golden brown. Drain the potatoes on a paper towel or absorbent cloth. Sprinkle with salt and pepper while hot.
To make 'frizzled leeks': Cut the 3-inch piece of leek into matchstick slices similar to the potato. Place the potato starch in a small bowl, lightly dust the leek pieces in it to help prevent them from burning. Fry the strips of leek in the same hot oil used for the potatoes, until they are just golden, about 1 minute
Add to the bowl of matchstick fries. Mix them together. Garnish in a little mound on top of the soup.