In a large, heavy-bottomed stock pot, over medium heat, add the olive oil, the sausage, and the onion. Saute, stirring occasionally for 30 minutes. Remove the sausage from the pot and transfer to a paper-towel lined colander. You will want to drain the grease well.
Add the chicken stock, potatoes, rosemary, and thyme to the pot. Bring to a low boil. Boil until the potatoes are just done -about 25 minutes.
Remove the thyme and rosemary sprigs.
Add the sausage and onion mixture back to the pot. Add the heavy cream and stir well to combine.
Bring the soup back to a low boil. Once the soup begins to bubble slightly, turn off the heat and place a lid on the pot. Allow the soup to sit for 5 minutes.
Remove the lid. Stir about a teaspoon of fresh thyme leaves and serve immediately.
Grated cheddar cheese is a great topping for this soup!