Warm the olive oil in a soup pot over medium heat and add the onions, carrots, and celery. Stir and cook for about 3 minutes or until the onions are translucent, then add the diced potatoes
Cook for 5 minutes, seasoning with salt and pepper.
Add the broth and bring it to a gentle boil. Cook 10 minutes, or until the potatoes start to become tender. Whisk the flour and milk together, then pour into the soup and cook for another 5 minutes.
Remove 1/2 to 2/3 the soup and blend in batches in a blender/ food processor until completely smooth. Please always use caution when blending hot soup, in fact, we recommend that you allow the soup to cool, if possible. If you have one, use an immersion blender instead of a stand blender or food processor.
Return the blended soup to the soup pot and heat it to adjust seasoning. Stir in cream, then parsley, and reserve a bit of parsley for garnish.
Serve with a a bit of fresh EVOO on top, and finish with balance of chopped parsley.