Heat the vegetable oil in a large pot over medium heat. Add the sliced onion and sauté until translucent, about 3-4 minutes.
Add the Wagyu beef pieces to the pot and brown them on all sides, about 5 minutes.
Stir in the sliced burdock root and grated ginger, cooking for an additional 2 minutes.
Pour in the soy sauce, mirin, sake, sugar, and water. Stir to combine, then bring the mixture to a gentle boil.
Once boiling, reduce the heat to low, cover the pot, and let it simmer for about 45 minutes, stirring occasionally.
After 45 minutes, remove the lid and let it simmer uncovered for another 15 minutes to thicken the sauce slightly.
Serve hot over steamed rice or with your favorite side dishes.