Wrap the tofu in a clean tea towel, place something heavy (such as a pan) on top of it to force out the excess water, then leave it for about 30 minutes.
Heat 1 tbsp. of oil in a sauté pan, add the chopped onion and sauté for about 5 minutes over medium heat.
Place the drained tofu in a bowl and mash well. Add the fried onion, miso, egg and nutmeg. Mix well. Mix in the panko bread crumbs. Dived the mixture into fourths and shape into four burgers.
Heat the remaining 2 tbsp. of oil in a sauté pan, and fry both side of the tofu burgers over medium heat until golden on both sides.
To make the miso mayonnaise, combine the mayonnaise and miso in a small bowl.
Serve the cooked burgers in toasted buns with the miso mayonnaise, lettuce, tomato and red onion. Add your favorite additional burger condiments.