Heat a Dutch oven over medium heat. Add the butter, followed by the celery and leeks. Continue cooking, stirring occasionally, until the vegetables have softened but are not browning, 3 to 5 minutes.
Add the wine to the vegetables and let reduce by half. Add the potatoes and stir to combine. Add the clam juice, 1 cup water and the reserved oyster liquor. The potatoes will soak up some of the saltiness of the oysters and their liquor, giving them great flavor. Bring to a simmer, cover and continue cooking until the potatoes are tender, 6 to 7 minutes.
Remove 1 1/2 cups of the soup, blend until smooth in a blender or food processor and return to the pot. Stir in the half-and-half and seafood seasoning. Season with salt and pepper. Bring to a simmer before adding the oysters. Cook just until the oysters begin to curl, 2 to 3 minutes. Remove from the heat and garnish with parsley. Serve with oyster crackers.
When blending hot liquids, make sure there is a vent on top for the steam to escape. Place a towel over the hole and start the blender slowly to avoid an explosion.