Bring 2 1/2 cups water to a rolling boil. Once boiling, add the 2 Cups rice and remove form heat, cover and simmer for 20 minutes. Then remove cover and let stand 5 minutes for rice to absorb remaining water.
While waiting for the water to boil and rice to simmer, add all the ingredients for the white sauce in a medium bowl, whisk together and chill covered until ready to serve.
Hibachi Chicken or Steak: Slice the meat and vegetables into bite size pieces. Spread 1 Tb vegetable oil in 2 separate large skillets over medium high heat. Now in one large skillet, melt 1 TB butter and then add 1 TB soy sauce and the chicken or steak and saute over medium/high heat and add a dash of salt and pepper. Stir often.
In the other large skillet, add portions of the bite sized vegetables (onion and zucchini, not mushrooms) with 1 TB butter, 2 TB soy sauce, dash salt and pepper. (1 TB butter, 2 TB soy sauce, dash salt and pepper for each 1 to 2 cup portion, or unless the portions are small use like 1/2 the ingredients). Cook each portion for about 7 to 8 minutes or until desired tenderness. Cook in portions unless you have a hibachi grill or large enough skillet to cook all the vegetables at once. Stir occasionally. I'm usually cooking for 6 so I have to cook portions separately or else half the vegetables will end up being over cooked while the other half is not cooked at all. Once you've made this recipe more than once you will be able to cook more at a time, just don't overwhelm yourself.
When the chicken (add a little lemon juice at the end) or steak is done, add mushrooms and 1 TB butter, 1 TB soy sauce or more if you have decided to cook a lot of mushrooms.
Continue to stir both pans.
Spoon the vegetables into even portions onto everyone's plates, and the meat into even portions then use one of the meat or vegetable's now empty skillet for the rice.
Toss the scrambled eggs, grated carrots, peas, diced onion with the cooked rice and melt about 1 1/2 or 2 TB butter in the skillet and spoon (slotted spoon) the rice mixture over into the skillet with melted butter, frying it over medium high heat. Add soy sauce and salt and pepper. Cook for about 8 or so minutes stirring as often as you can to keep rice from burning.
Serve in even portions to everyone's plates.
Serve white/orange dipping sauce as you'd like. In my family we use generous amounts over the entire plate.