Add all the ingredients for the sauce in a bowl and stir until the sugar has dissolved.
In a medium sauce pan over medium high heat, add the sauce, onions, shiitake mushrooms, carrots and cabbage and lower the heat to a simmer.
Simmer for 10 minutes, until vegetables are cooked but still yielding a little crunch. This dish is good when the veggies aren’t overcooked since it will be served over rice. The balance of slightly crunchy and soft will pair well together.
Briefly beat the eggs using chopsticks and slowly drizzle evenly into the sauce pan. Cover and cook for a couple of minutes until the eggs are almost cooked, slightly runny. There should also be some soup left.
Fill two bowls with warm Japanese rice and top them with the vegetable oyakodon.
Top with extra sauce if you want more flavor, mitsuba and a little shichimi togarashi.