Heat oil in skillet and add onions, carrots, and celery, stirring occasionally until starting to soften. Add mushrooms and cook about two to three minutes. Add the soy sauce and cook until the mixture is tender and no more liquid remains. Set aside to cool.
To a medium-large bowl, add ground beef and the rest of the ingredients. Add the cooled vegetable mixture. Toss lightly to combine, take care not to compress the beef.
Mixture will be very moist. Form into eight oval egg-shaped loaves with curved tops (easiest done by estimating half of the mixture, then half again and so on.) Place on foil-lined rimmed sheet (foil is optional, but makes for easy clean up) an inch or so between each loaf.
Bake at 350 degrees to desired doneness, about 20 to 25 minutes to reach 160 degrees depending on oven. Do not over bake.
Note: to freeze, lay each loaf on a piece of plastic on a flat surface. Freeze until hard, then use the plastic wrap to wrap each individual loaf. Add to a Ziploc and label. Thaw overnight in the fridge to bake the next day.