In a stockpot (porcelain-lined cast iron works great), heat oil over medium heat. Add onions and cook, stirring occasionally, until softened, 3 to 5 minutes.
Add tomatoes and cook until most of the liquid evaporates, 3-4 minutes. Sometimes the mixture may look a little dry, but don't add any extra liquid--the cabbage will give off moisture.
Add potatoes, cabbage, dill, vinegar, salt and pepper.
Reduce heat to medium-low. Cover and cook for 20 minutes. Add the sun-dried tomatoes and continue to cook until potatoes are tender, abouve 10-20 more minutes. Check seasonings adding more salt and pepper if needed.
Remove from heat and stir in sour cream. Serve immediately.