Heat the olive oil in a large pot over medium heat. Add the chopped onion and sauté for about 5 minutes, or until translucent.
Add the minced garlic and cook for an additional 1 minute, stirring frequently to avoid burning.
Incorporate the diced potatoes into the pot and stir well to combine with the onions and garlic.
Pour in the vegetable or chicken broth, ensuring the potatoes are fully submerged. Bring the mixture to a boil.
Once boiling, reduce the heat to low and simmer for 20-25 minutes, or until the potatoes are tender.
Using a potato masher or immersion blender, mash or blend the soup to your desired consistency. You can leave it slightly chunky or blend it until smooth.
Stir in the heavy cream, salt, black pepper, and dried thyme. Let it simmer for an additional 5 minutes to heat through.
Taste and adjust seasoning if needed.
Serve hot, garnished with chopped chives or green onions if desired.