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Wash and trim asparagus; cut stalks into pieces and set tips aside.
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In large, non-stick saucepan, heat oil; saute garlic, onion, leeks, and asparagus stalks just until softened, approximately 10 minutes.
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Add stock and potatoes; reduce heat, cover and simmer for 20-25 minutes or until vegetables are tender.
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Puree in food processor until smooth OR cook a little longer until potatoes begin to break apart and forego the processing (personally I prefer the chunkier consistency).
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Taste and adjust seasoning with salt and pepper.
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Return to saucepan (if you chose to process the mixture).
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Steam reserved asparagus tips until just tender (approx. 2 mins); add to soup.
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ENJOY! :-).