Heat up the oil over medium heat in a soup pot.
Add the onions and rosemary. Cook on medium heat for 10 minutes, stirring occasionally.
Add the potatoes, salt and stock and bring to a boil. Lower the heat, cover and simmer for 10 minutes.
Add the spinach, basil and parsley, cover and simmer for 1-2 more minutes.
Turn off the heat and add the cheeses, milk, and pepper.
Use an immersion blender to thoroughly blend everything together, leaving no chunks or leaves unblended.
Ladle into individual bowls and top with additional cheese, salt, and pepper.