Place potatoes in a large saucepan, cover with cold, heavily salted water, and bring to a boil over high heat. Reduce heat to medium low, and simmer until potatoes are just tender. Drain and let potatoes cool.
When potatoes are cool enough to handle, slice into 1/8-inch rounds. Combine with onion, celery, and fennel in a large mixing bowl. In a small bowl, whisk together vinegar and oil, and season well with salt and freshly ground black pepper. Pour over potato mixture, add parsley, and toss to coat. Taste and season with additional salt and pepper as needed.
Beverage pairing: Petaluma Hanlin Hill Riesling, Australia. Fennel is a flavor that can often be detected in Australian Rieslings, so it is a good call for this dish. This wine is bone dry, and its notes of tea and lime will hit it off with the celery and parsley, its sharp acidity will help to balance the vinaigrette, and its earthy finish will be good with the potatoes.
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