Slice leeks lengthwise and wash out any dirt between the layers. Chop and place in a large mixing bowl with garlic.
Melt butter in a large soup pot over medium heat. Add leeks and garlic and cook, stirring frequently, for 5 minutes. Add potatoes, vegetable broth, Italian seasoning, and rosemary. Bring to a boil; reduce heat and simmer for 20 minutes.
Remove from heat and let soup cool briefly. Transfer mixture to a blender or food processor and puree in batches. Return soup to the pot and stir in half and half and season with black pepper. Reheat gently, about 5 minutes.
Light Potato and Leek Soup · Dinner Match Lab | Dinner Match Lab