Cut the tofu into 3 sections lengthwise. Using paper towel, press onto the tofu to remove any excess moisture. Flip the tofu over and repeat until you can get most of the moisture out.
Using your hands, crumble the tofu into a large bowl and add with the chopped onion.
In a small bowl, combine the dijon mustard, yellow mustard, mayo, relish, apple cider vinegar, lemon juice, parsley, celery seed, sea salt and pepper. Stir with a spoon until combined thoroughly.
Pour the sauce over tofu mixture and stir to combine.
Scoop the "egg" salad onto bread and enjoy.