In a large pot or Dutch oven, cook the sliced sausage over medium heat until lightly browned. Remove the sausage with a slotted spoon and set aside, leaving about 1 tablespoon of drippings in the pot.
Add the olive oil to the pot if needed. Add the chopped onion and celery. Cook until softened, about 5 minutes.
Add the minced garlic and cook for 1 minute until fragrant.
Sprinkle the flour over the vegetables and stir constantly for 1 minute to cook out the raw flour taste. This creates the roux for thickening.
Gradually whisk in the chicken broth until smooth. Bring the mixture to a simmer, stirring often.
Add the diced potatoes, thyme, salt, and pepper to the pot. Return the sausage to the pot.
Bring the chowder back to a simmer, then reduce the heat to low, cover, and cook for 15 to 20 minutes, or until the potatoes are tender when pierced with a fork.
Stir in the heavy cream. Heat through gently for 2 to 3 minutes; do not boil after adding the cream.
If using, stir in the shredded cheddar cheese until melted and the chowder is creamy.
Taste and adjust salt and pepper as needed. Serve hot, garnished with fresh parsley.
Notes
For a thicker chowder, mash about one cup of the cooked potatoes against the side of the pot before adding the cream.
You can substitute smoked turkey sausage for a lower-fat option.