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In a large stock pot, heat olive oil and sauté onion until tender, about 5 minutes. Add garlic and cook for 2 minutes. Add potatoes,vegetable broth, and water to the pot. Bring to boil and reduce to medium heat. Let potatoes cook until tender, about 20 minutes. With a slotted spoon, remove 2 cups of the potatoes. Set aside. Puree the remaining potatoes with an immersion blender or put potatoes in a blender or food processor.
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In a small sauce pan, melt butter. Stir in flour and cook for 2 minutes. Whisk in milk, bring to a boil and simmer until thickened. Slowly stir mixture into large stock pot with the pureed potatoes. Bring to a boil and reduce heat to a low simmer. Stir the 2 cups of potatoes back into the soup.
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Stir in feta cheese and fresh rosemary. Season with salt and pepper, to taste. Cook for an additional 5 minutes. Serve warm.