Heat the oil in a large skillet over medium heat. Add the onions and saute until softened but not coloured, 5-7 minutes. Stir in the paprika and toss with the onions.
Add the peppers and continue to saute, stirring occasionally, for another 10 minutes. Do not allow the vegetables to brown.
Stir in the tomatoes, tomato paste, broth, kielbasa, salt and pepper. Allow the mixture to boil, reduce the heat, cover, and simmer the peppers until very tender, about 30-35 minutes.
Off the heat, stir in the vinegar and sugar and allow the mixture to cool.
Serve warm, at room temperature, or cold garnished with chopped parsley.