Heat 1 Tbsp olive oil in a large pan on medium-high heat and sauté the onion until translucent.
Turn off the heat and divide the sautéed onion in half (half for the gravy and half for the patty).
To Make Gravy
Cut mushrooms into thin slices. Heat ½ Tbsp olive oil in a small saucepan on medium heat and sauté mushrooms till soft. Add half of the sautéed onion and stir together.
Add 1 ½ cup beef stock, 1 tsp Worcestershire sauce, and 1 tsp soy sauce.
Skim any foam or scum on the surface. Season with salt and freshly ground black pepper.
In a small bowl, combine 1 Tbsp potato/corn starch and 1 Tbsp water and whisk well to mix together. Pour the potato starch mixture into the gravy and thoroughly mix together. Simmer till the gravy is a bit thicker. Turn off the heat and set aside.
To Make Patties
In a large bowl, add the meat and the rest of the sautéed onion. Add ⅓ cup panko, an egg, 2 Tbsp milk, 1 tsp Worcestershire sauce, ½ tsp nutmeg, 1 tsp salt, and black pepper.
Mix the meat well until the mixture gets sticky and pale, and then divide into 4.
Make 4 large patties (or 6 medium patties if you like). Toss each portion of mixture from one hand to the other hand repeatedly about 5 times in order to release air inside the mixture. If you don’t release the air inside, the meat patties will crack. After tossing, make oval shape patties. The top should be slightly round and not flat. Keep the patties in the fridge for at least 30 minutes before cooking so that the meat combines together.
In a large pan, heat ½ Tbsp olive oil over medium heat and place the patties gently on the pan. Indent the center of each patty with 2 fingers because the center of patties will rise with the heat. Cook the patties for about 5 minutes. Do not flip until the bottom of the patties is nicely browned. Cover and cook for 5 minutes to thoroughly cook the inside of the patties (adjust cooking time depending on patty’s thickness). You can also re-heat the gravy and make fried eggs at this time.
Serve steamed rice on individual plates. Transfer the patties to the plates, pour the gravy, and top with a fried egg. Serve immediately.
You can keep the leftovers in an airtight container and store in the refrigerator for 3 days or in the freezer for a month.