Bake, boil, microwave, or pressure cook potatoes until tender. Run under cold water to remove skins. Chill.
Meanwhile, steam tofu for 10 minutes. While tofu is cooking, place rice vinegar (lemon juice), oil (if desired), tamari, mustard, salt and garlic in a blender or food processor. Blend until smooth.
Drain tofu, crumble and add to blender or food processor along with dill. Blend until smooth and creamy. You may need to add a few tablespoons of water (up to 1/4 cup) depending on how soft the tofu is and how well your blender purees. You will want it a little "loose" and liquidy, as the potatoes will absorb some of the moisture.
Chop chilled potatoes into 1-inch cubes and place in a large mixing bowl. Pour tofu mixture on top of potatoes and mix, evenly coating potatoes. Stir in celery and parsley. Be careful not to mash potatoes as you mix.
Makes 6 side-dish servings.