Preheat your Dutch oven over medium heat.
Add the olive oil to the Dutch oven and heat until shimmering.
Add the leeks and cook, stirring occasionally, until softened, about 5 minutes.
Add the garlic, thyme, salt, and pepper and cook for 1 minute more, until fragrant.
Add the potatoes and chicken broth and bring to a boil.
Reduce heat and simmer, covered, for 20 minutes, or until the potatoes are tender.
Using an immersion blender or regular blender, purée the soup until smooth.
Stir in the heavy cream and heat through.
Garnish with chopped fresh parsley, if desired.