In a large pot, add butter to medium-high heat. Add leeks and cook for 20 minutes, until leeks have softened.
Add roasted garlic, sprig of thyme, chopped potatoes, broth, and seasoning. Cover and cook for 20-25 minutes, until potatoes are soft. Remove sprig of thyme. Remove soup from heat (or transfer in batches to blender)
Puree soup. Add 1 cup of milk while pureeing. Return to pot and bring to a boil. Taste for seasoning and adjust if needed.
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