Wrap drained tofu in a clean, lint-free dish towel and place on a plate. Set another plate or block of butter on top. Place in the refrigerator to drain for 30 minutes.
Preheat oven to 350 degrees F (175 degrees C). Line a small baking dish with parchment paper.
Unwrap tofu and discard accumulated liquid. Cut tofu widthwise into 4 equal pieces. Carve each piece into the shape of half an egg white using a spoon. Hollow out the center of each piece to create a spot for the "yolk." Reserve all the scraps.
Marinate "egg whites" in cider vinegar in a shallow dish for 10 to 15 minutes. Remove from vinegar and transfer to the prepared baking dish.
Bake tofu in the preheated oven for 10 minutes.
Combine tofu scraps, chickpeas, mustard, nutritional yeast, cayenne pepper, salt, and pepper in a food processor; blend until smooth. Spoon mixture into a resealable plastic bag and snip off one corner.
Pipe the chickpea mixture into the hollows in the tofu. Garnish with chives and paprika. Chill before serving.