Frying leeks: Cut leeks crosswise into 2-inch lengths. Then cut lengthwise into enough very thin strips to measure 2 cups. Wash the leek strips in a bowl of very cold water, agitating them; lift out and pat thoroughly dry.
In a deep 4-quart heavy saucepan, heat the vegetable oil until it registers 350 degrees F. on your cooking thermometer. Fry leeks in 8 batches, stirring, until golden, approximately 10 seconds per batch. As the leeks are fried, remove with a slotted spoon to paper towels to drain. Let cool completely (leeks will crisp as they cool) before using; Set aside. NOTE: Fried leeks can be made 3 days ahead and kept in a sealed plastic bag at room temperature.
Making Oyster Soup:
Drain the oyster liquor (juice) off the oyster into a bowl. NOTE: I like to strain the oyster liquor with a fine strainer to remove any sand. Add enough bottled clam juice to bring the total to 1 1/2 cups of juice. Pick over the oysters, discarding any bits of shell and then rinse them well; set aside. Peel potatoes and cut into 1/2-inch cubes; set aside.
In a large 4-quart heavy saucepan over low heat, heat the butter. Add the leeks, potatoes, and 1 teaspoon salt; cook, covered and stirring occasionally, until the leeks are golden and the potatoes are just beginning to soften, approximately 15 minutes. Raise heat to medium, add the water and let simmer, covered until potatoes are very tender, approximately 10 minutes. Remove from heat and let cool slightly before pureeing.
In a blender or food processor, puree the soup in batches until very smooth (use caution when blending hot liquids). Transfer each batch to a large bowl. NOTE: The pureed soup base (without the oysters, oyster liquor, cream, and cayenne pepper can be made 2 days ahead. Let soup base cool, uncovered, then refrigerated, covered, until ready to use.
Return the pureed soup to the saucepan. Add oyster liquor and cream. Over medium-low heat, let simmer approximately 1 to 2 minutes, stirring occasionally (do not boil). Add the oysters and cayenne pepper and cook, stirring occasionally, just until the oysters become plump and the edges curl, approximately 3 minutes. Season with salt to taste. Be careful to avoid overcooking oysters, which causes them to become tough.
To Serve: Ladle the Oyster soup into individual soup bowls and then top with some of the fried leeks.
Makes 8 servings (about 11 cups).
* Cut and clean leeks: You need to thoroughly clean a leek because dirt can become trapped in its many layers. Trim the root portion right above the base (cutting too far up the stalk will remove the part that holds the layers together. Slice off the fibrous green tops, leaving only the white-to-light green stalk. Discard greens. Cut the leek in half lengthwise, then cut according to your recipe (slice, chop or dice). For this recipe, cut the leeks into 2-inch lengths.
** Only use small oysters, 1 to 1/2 inches in diameter in this recipe. Larger ones will make the flavor too briny. How To Shuck Oysters.
Oyster Soup With Frizzled Leeks Recipe: https://whatscookingamerica.net/LindaSandberg/Soups/OysterSoup.htm