Heat oil in large dutch oven. Brown sausage in batches, about 1 minuter per side. Remove to plate and set aside.
Add the carrots, onion and leeks to the pot and soften in batches (about 5 minutes). Season with salt and pepper.
Return vegetables and sausage to the dutch oven. Add chicken stock, bay leaves and potatoes. Simmer at least 30 minutes. A couple of hours is even better.
Remove bay leaves. Remove about 2 cups of vegetables and liquid (carefully avoiding sausage) and place in a bowl. Add heavy cream and process with an immersion blender. You can use a regular blender or a food processor but be careful with hot liquid.
Return smooth vegetables to pot. Blending a bit of the vegetables with cream gives you a little thicker and richer soup.
Serve with crusty bread.