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In a large kettle, cover the potatoes with water, bring to a boil over high heat, then reduce the heat to medium-low and boil gently for 30 minutes, or just until the potatoes are tender, but not overcooked.
Meanwhile, prepare the olives, pickles, onions, and celery, setting them aside in a small mixing bowl.
If you still have time, jump ahead and prepare the dressing, again setting it aside until needed.
When the potatoes have finished cooking, replace the hot water with icy cold water, leaving the kettle under the faucet with the cold water running until the potatoes are cool enough to handle, then drain.
Peel the potatoes, if desired (I often leave at least part of them unpeeled), then cut into 1/4-inch slices, spreading the slices evenly into a 13x9x2-inch pan.
Place the drained tofu on a cutting board.
Using a sharp knife, cut crosswise into 1/4-inch slices, then cut through the tofu again – this time lengthwise, at 1/4-inch intervals.
(You should be left with fat, somewhat short, matchstick-shaped pieces that look very much like cooked egg white).
Spread the tofu evenly over the potatoes.
Using a pastry blender (or two knives), cut firmly through the tofu and potatoes several times, just until coarsely chopped.
(Some of the pieces of tofu should remain large enough – even after folding in the dressing, to look liked chopped egg white).
Spread the prepared olives, pickles and onions evenly over the tofu and potatoes.
To make the dressing:
In a small mixing bowl, whisk together all of the dressing ingredients, then pour the dressing over the salad ingredients.
Lightly fold the dressing into the salad ingredients, just until the salad is well mixed, again taking care not to break up the tofu too much.
(Add a little more pickle juice, if needed).
Cover and refrigerate.
(Salad is best if refrigerated for several hours before serving).
Before serving, transfer the salad to a serving bowl.
Garnish with parsley flakes and paprika.
Serve cold.
Refrigerate leftovers.