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1
Trim the stringy root ends and all but 1/2 inch (12 mm) of the stalks from the bulbs of green garlic. Peel away the outer layer from the bulbs and chop the bulbs.
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2
In a saucepan, melt the butter over medium-high heat. When it foams, add the garlic and shallot and cook, stirring, until soft, about 3 minutes. Add the broth and bring to a boil, then reduce the heat to low and simmer until the broth is infused and the garlic is exceedingly soft, about 4 minutes.
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3
Place a chinois or fine-mesh sieve over a clean saucepan and strain the garlic broth, pressing on the garlic and shallot with the back of a spoon to extract the maximum flavor. Discard the solids. Return the strained garlic broth to the saucepan, add the potatoes, and bring to a boil over medium-high heat. Reduce the heat to medium and cook until the potatoes are soft and easily pierced with the tines of a fork, about 20 minutes.
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4
Using an immersion or upright blender, puree the soup until smooth. Over a clean saucepan, strain once again through a chinois or fine-mesh sieve, gently pressing against any remaining solids.
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5
Place the saucepan over medium heat and bring the puree to just below a simmer. Stir in the salt and pepper, followed by the creme fraiche. Taste and adjust the seasoning. Ladle the soup into bowls and serve at once.
