Japanese Hamburg Steak - Hambāgu

1 large egg
1 small onion finely diced
1 large clove garlic minced
1 lb. ground beef
6 oz. soft tofu - soft
1 cup panko
2 tbsp. ketchup
1 tbsp. oyster sauce
1 tbsp. parsley minced
1 tsp. soy sauce
1/4 tsp. black pepper
1/2 cup dry red wine
1/4 cup ketchup
1/4 cup water
2 tbsp. tonkatsu sauce Worcestershire sauce also works
1 tbsp. demi-glace - optional

Add a tablespoon of vegetable oil to a frying pan and sauté half the onions and all of the garlic until medium brown and caramelized. Let these cool to room temperature.
Combine the beef, tofu, sauteed onions, raw onions, panko, egg, 2 tablespoons of ketchup, oyster sauce, parsley, soy sauce and black pepper in a large bowl. Vigorously knead the mixture together until it is uniform in color and texture. Add more oil to the frying pan that you fried the onions in and place over medium heat. Because the patties are on the soft side, you'll want to form them and add them directly to the pan. Make about 8 oval patties about 1" thick.

Fry them until they've formed a dark brown crust on one side, then use a spatula to carefully flip them over and brown the other side. Unless you have a very large pan, you won't be able to do them all at once, so fry 4 at a time and transfer them to a plate when they're browned on both sides. Don't worry if they're not cooked all the way through as they will finish cooking in the sauce.
After you've fried all the patties, drain off any excess oil but don't wash the pan as the brown stuff is what will give your sauce flavor. Add the red wine and boil until it's reduced by about half in volume.

Add the ketchup, water, tonkatsu sauce, and demi-glace and stir to combine.
Place the patties back into the pan, cover, and cook for 7 minutes, flipping them over once in the middle. Cook uncovered for another 3 minutes to thicken the sauce a little. Serve with rice.