1. In a large pot, heat the olive oil over medium heat. Add the sliced onions and minced garlic, sautéing until the onions are soft and translucent.
2. Add the chopped artichoke hearts to the pot and continue to sauté for an additional 5 minutes.
3. Pour in the vegetable or chicken broth and add the diced potato. Bring the mixture to a boil, then reduce the heat and simmer until the potato is tender, usually about 15-20 minutes.
4. Use an immersion blender to puree the soup until smooth. Alternatively, transfer the soup to a blender in batches, blend, and then return it to the pot.
5. Pour in the milk or cream, stirring well to combine. Adjust the consistency with more broth or milk if needed.
6. Season the soup with salt and pepper to taste. Adjust the seasoning as necessary.
7. Allow the soup to simmer for an additional 5-10 minutes to let the flavors meld.
8. Serve the Artichoke and Onion Soup hot, garnished with fresh parsley if desired.

Enjoy your delicious Artichoke and Onion Soup!