In a Dutch oven, heat 2 tablespoons oil over medium high heat. Add pork and cook for 4 minutes or until browned, stirring occasionally. Remove pork from pan and set aside.
Using the same pan, add remaining 2 tablespoons oil and heat over medium heat. Add red bell pepper and onion and cook for 5 minutes, stirring occasionally.
Add ginger, garlic, and black pepper; stir and cook for 30 seconds. Add 7 cups of the broth.
In a small bowl, gradually whisk remaining 1 cup broth with miso paste. Add miso mixture to the pan and bring to a boil.
Add soybeans and pork to the soup. Bring to a boil, reduce heat and then simmer, covered, for 3 minutes.
Add cabbage and cook for 2 minutes more, stirring occasionally.
Correct seasonings with salt and pepper to taste.
Ladle soup into individual bowls and serve garnish with radish slices.