Heat olive oil in a large stock pot.

Saute diced onion until tender, about 5 minutes.

Add minced garlic and cook for 2 minutes.

Add cubed potatoes, vegetable broth, and water to the pot.

Bring to a boil, then reduce heat to medium.

Cook potatoes until tender, about 20 minutes.

Remove 2 cups of potatoes with a slotted spoon and set aside.

Puree the remaining potatoes using an immersion blender or a regular blender/food processor.

In a small sauce pan, melt butter.

Stir in flour and cook for 2 minutes to create a roux.

Whisk in milk, bring to a boil, and simmer until thickened to form a béchamel.

Slowly stir the béchamel into the large stock pot with the pureed potatoes.

Bring to a boil and reduce heat to a low simmer.

Stir the reserved 2 cups of potatoes back into the soup.

Stir in feta cheese and fresh rosemary.

Season with salt and pepper to taste.

Cook for an additional 5 minutes to allow flavors to meld.

Serve warm.