For Mayonnaise: Whip first 5 ingredients in a blender or food processor. Keep the machine going and gradually add in oil. Continue to whip until creamy texture is reached.
Cut the tofu into dice-sized bits and add to bowl with scallions, carrot, celery, pepper, and seeds.
Gently mix in eggless mayo.
Spread salad onto bread and top with a mound of sprouts or mixed greens.