Whisk the sauce ingredients together in a small bowl and set aside.
In a large Wok or Skillet (I use nonstick, Gochujang tends to get sticky) over medium high heat add the oil.
When pan is hot add the meat and onions keeping them separated in the pan. Do not turn over and mix together until one side starts browning.
When meat and onions are nicely browned lower heat to medium and add Shiitake mushrooms and the sauce mixture and cook together until blended well, about two minutes.
Add the cooked udon noodles, stirring carefully. Do not over mix, let noodles simmer in the sauce for about 2 minutes making sure the sauce is completely coating the noodles.
Add the scallions at the end and mix gently for another minute.
Divide noodles between two plates and top each serving with an egg.
DONE