Combine the ponzu sauce and the ketchup in a small saucepan. Add oregano. Heat to medium heat and simmer to reduce liquid, about 5 minutes. Set aside.
Finely chop the radish and add to slightly cooled sauce (if using).
Heat the olive oil and butter in a frying pan. Saute green bell pepper, onion, and cabbage over medium heat until tender and starting to brown, 5-8 minutes. Remove to serving plate, spreading out just a little to make nest for egg.
In same pan add the 1 teaspoon oil or butter and saute the egg to desired doneness(turning over once).
Place the egg over the sauteed veggies. Drizzle with the sauce(I used several tablespoons). Dig in and enjoy!