In a large pot, heat some oil over medium heat. Add the onion and garlic and cook until softened.
Add the diced potatoes, dried thyme, salt, and pepper to the pot. Stir to coat the potatoes with the seasonings.
Pour in the chicken broth and bring to a boil. Reduce heat to low and simmer for about 20 minutes, or until the potatoes are tender.
Using a potato masher or immersion blender, mash the potatoes until desired consistency is reached.
Stir in the milk and heavy cream and heat through. Taste and adjust seasoning if needed.
Serve the potato soup hot, garnished with chopped fresh parsley.