• Finely chop the onion. Heat oil in a pan, add the onion along with salt, and sauté over medium heat until softened and translucent. Once softened, remove the pan from the heat and let the onion cool to room temperature, either in the pan or by transferring it to a separate dish to speed up the cooling process.
  
• In a bowl, combine the ground beef, ground pork, salt, black pepper, and nutmeg. Knead the mixture until it becomes sticky and cohesive. Once it reaches this stage, add the cooled onions, egg, panko breadcrumbs, and milk, and continue kneading until everything is well combined.
  
• Divide the mixture into equal portions according to the number of hambagu you want to make (I divided mine into three portions). Take one portion and shape it into a ball, then gently toss it back and forth between your hands about 10-20 times, as if playing catch, to remove any air pockets. Shape each portion into an oval or round patty about 1 inch (2.5 cm) thick. (In Japan, a typical patty weighs about 3.5-5.3 ounces / 100-150 g.)
  
• Heat oil in a pan. Once the pan is hot, place the patties in it and cook over medium heat for about 2 minutes until browned. Flip the patties and cook for another 1 minute 30 seconds until browned on the other side.
  
• Add water (as specified in the ingredient list) to the pan and cover with a lid. Reduce the heat to low and let it steam for about 5 minutes. Turn off the heat and let the patties rest with the lid on for at least 3 minutes to allow the juices to redistribute.
  
• Serve the hambagu with vegetables if desired. You can enjoy it as is, but it is typically served with ketchup or a special sauce.

  Here is a recipe for a ketchup-based sauce you can try:
  

To make a ketchup-based sauce:

• Add sake, ketchup, and Worcestershire sauce to the pan used to cook the patties and simmer over medium heat for about 1 minute, stirring to combine. Then, turn off the heat, add butter, and stir until melted and smooth.