Season beef wiht salt and pepper the beef, then add it to the hot oil. Fry undisturbed for a few minutes or until the beef has a golden brown crust on one side, then flip the beef and fry until browned on the second side. The browned crust is were the flavor is at, so the more crust the better.

Transfer the beef to a plate and set aside. Add some more oil if needed, then add the onions and garlic. Cover with a lid and cook over medium low heat for 10 minutes. Remove the lid, then add the baking soda if you want to speed up the caramelization process. Fry the onions, stirring frequently until it's about 1/6 of the original volume, and is dark brown and glossy. If you add baking soda, this should take about 20 minutes, if you don't, it will take about an hour.

Return the beef to the pot along with the wine, water, bay leaf, cloves, tomato past, tonkatsu sauce, demi-glace, soy sauce, and paprika, along with the mushrooms and onions. Partially cover with a lid and cook for 1-2 hours or until the beef is very tender. While the beef is cooking, heat the butter and flour in a small saucepan over medium high heat. Stir continuously until the butter is melted, then stop stirring until the mixture starts taking on a color. Continue cooking and stirring

When the beef is tender, turn the heat down to low, add the roux a spoonful at a time and stir vigorously to keep it from clumping. The hayashi rice should start getting thick pretty quickly (you might not need all the roux). Stop when you're happy with the thickness.