Step 1

Heat oil in a large saucepan or Dutch oven over medium heat until shimmering. Add sausage and cook, stirring occasionally, until well browned, about 5 minutes. Remove sausage from pan using a slotted spoon, leaving any rendered fat behind. Set sausage aside.

Step 2

Add butter and leeks to sausage fat in the saucepan. Season with salt and pepper and cook, stirring, until leeks have softened but not browned, about 3 minutes, reducing heat if necessary. Add potatoes and chicken stock, scraping up any browned bits from the sides and bottom of the pot. Add cabbage and bay leaves. Increase heat to high and bring to a boil. Reduce heat to maintain a bare simmer and cook until potatoes are completely tender, about 10 minutes.

Step 3

Add sauerkraut and its liquid to the pot and bring to a simmer. Discard bay leaves. Working in batches, transfer the soup to a blender and blend, starting at lowest speed and slowly increasing to maximum speed, until soup is completely smooth, about 2 minutes per batch. Transfer the soup to a fine-mesh strainer set over a clean pot, using the back of a ladle to push it through. Season to taste with salt and pepper.

Step 4

Garnish soup with browned sausage pieces, chopped dill, and olive oil. Serve immediately with crusty bread.