Heat the olive oil in a soup pot. Remove the sausage from its casing, add it to the pot, break it up with a spatula, and cook until golden and cooked through. Remove the sausage to a separate plate.
In the same pot, add the chopped onion, sliced celery, and carrots. Cook over low heat for 10 minutes, then add the minced garlic and thyme. Cook for another 30 seconds.
Sprinkle the flour over the vegetables and stir to combine, forming a paste. Cook for a couple of minutes, then return the sausage to the pot.
Gradually pour in the chicken stock, stirring to combine with the roux. Add the bay leaves and wild rice, bring to a boil, and cook for 30 minutes.
Add the cubed potatoes and cook for another 15 minutes, until the wild rice and potatoes are tender. Pour in the cream, season with salt and pepper, and let the cream warm through before removing from heat.