In a large pot or Dutch oven, brown the sausage over medium heat, breaking it up with a spoon. Drain off any excess grease.
Add the olive oil, onion, and garlic to the pot. Cook until the onion is softened, about 5 minutes.
Pour in the chicken broth and add the potatoes, thyme, and pepper. Bring to a boil, then reduce heat and simmer until the potatoes are tender, about 15-20 minutes.
Stir in the heavy cream and heat through. Do not boil.