Stir together the water, beef and mushroom base, sugar, garlic, Worcestershire sauce, and soy sauce until thoroughly mixed.
In a skillet, saute the onion in the butter until softened, then stir in the flour, cooking briefly.
Add the water mixture all at once, and continue to stir until it comes to a boil and thickens, then remove from heat.
To make Loco Moco:
Shape Wagyu beef into four patties and season with salt and pepper.
Cook patties in a mixture of vegetable oil and toasted sesame oil until browned and cooked to your liking.
Steam or cook short grain sticky rice by your favorite method (I use a rice steamer).
Thinly shred green papaya and also thinly slice until it is a vermicelli. Toss with corn starch and fry over med-low heat until crisp and barely browned. Drain.
Fry eggs sunny side up in butter.
To assemble, place some sticky rice in a bowl; top with gravy and beef patty, then fried egg. Sprinkle with crispy papaya shreds and scallions along with a sprinkle of sesame seeds.