Heat the olive oil in a large pot over medium heat. Add the diced onion and sauté for about 8 minutes, or until soft and translucent.
Add 1/2 teaspoon salt and the minced fresh garlic. Cook for about 1 minute, stirring frequently so the garlic does not burn.
Pour in the vegetable broth and bring it to a boil.
Add the potatoes, parsley, black pepper, and remaining 1/2 teaspoon salt. Bring the soup back to a boil, then reduce the heat and simmer until the potatoes are completely tender.
Squeeze the soft roasted garlic cloves from the head and add them to the pot. You can mash the cloves first or add them whole since they will easily break down in the hot soup.
For a thicker Roasted Garlic Potato Soup, remove about 1 cup of the cooked potatoes and place them in a bowl. Mash them thoroughly with a fork, then stir them back into the soup.
Alternatively, use an immersion blender directly in the pot to partially blend the soup. Leave some potato pieces intact for a satisfying, rustic texture.
Taste and adjust the salt and black pepper as needed. Serve hot with chopped parsley, croutons, or your favorite cheese.