Fry bacon until crispy around the edges. Drain on paper towels and set aside. Reserve 1 tsp of the bacon fat, and use to saute the onion, shredded cabbage, bell peppers, and black pepper. Cook until vegetables are tender and lightly caramelized.
In a large saucepan, bring broth to a boil. Add the sauteed onion, cabbage and bell pepper mixture, along with the potatoes and carrots. Reduce heat, and simmer until the vegetables are tender, about 30 minutes. Remove from heat.
Using a slotted spoon, remove about 1 cup of cooked vegetables and set aside.
Use a stick blender (or a food processor) to blend the remaining mixture until smooth.
Stir the reserved cooked vegetables, basil and cooked bacon into the puree. (You may wish to save a bit of bacon for garnish) Simmer over low heat for 20 minutes.
Garnish with reserved cooked bacon, if desired.
Note: Depending on the variety of potato you use, you may need to add additional broth to thin the soup.