Put the onions in a microwave-safe bowl, cover the bowl and microwave at 800 watts for 4 minutes. You want them to be soft, and just starting to brown. Leave the onions covered and let them cool enough to handle.
In a separate bowl, add the panko, milk, oyster sauce, and black pepper and mix to combine.
When the onions have cooled a bit add them to the panko mixture along with the ground beef, and knead together until it's well combined.
Split the mixture in half and form them into 2 patties that are about a 3/4-inch (2cm) thick.
Place them on a plate or tray and make an indentation in the center to keep them from puffing up.
Prepare the gravy mixture by stirring the beef stock, soy sauce, Worcestershire sauce, and potato starch together.
Add the vegetable oil to a frying pan and heat over medium heat until hot. Break the eggs into the pan and then turn the heat down to low. Let the eggs fry until the white is cooked through and the yolk is done to your liking. Transfer the eggs to plate and set aside.
Add the hamburger patties to the pan you fried the eggs in and turn up the heat to medium. Fry the patties until they have a brown crust on one side and are cooked about a third of the way through (about 2 1/2 minutes). Flip the patties and fry until they're almost cooked through.
Transfer the patties to a plate and then add the mushrooms and onions. Saute until they are well browned and caramelized.
Add the rum and deglaze the pan.
Add the beef stock mixture and return the hamburger patties to the pan. Turn up the heat and boil the gravy until it has thickened, turning the patties over to glaze them evenly.
Finish the gravy by adding the cream and stirring to combine evenly.
To plate the Loco Moco, put down a mound of hot rice. Top with a beef patty, and then cover everything with gravy. Garnish your Loco Moco with fried shallots, and then place an egg on top.